Approved by the Government of Nepal, Ministry 5of Education, Science and Technology, Curriculum Development Centre, Sanothimi, Bhaktapur as an additional material.Please scan forE-book
Publisher : Sundar Pathshala Prakashan Pvt. Ltd.Anamnagar, Kathmandu, NepalLayout Design: Sundar Pathshala Prakashan DesktopEdition : 2063 (First)2067 (Second)2080 (Third)2083 (Fourth) Revised & UpdatedPrinted in Nepal
I feel proud to present this edition of Mathematics book. It is based on the latest syllabus, formed by Curriculum Development Centre (CDC). I have emphasized the theoretical as well as the numerical aspects of the mathematics course. The underlying concepts have been gradually and systematically developed.In each chapter, all the results and concepts of a particular topic have been put together. These are followed by a large quantity of solved examples. Quite a large number of problems have been given as exercises.I am thankful to Sundar Pathshala Prakashan Pvt. Ltd. for its contribution in bringing out this series in such a splendid form as well as thankful to staff who contributed in bringing out this series like as computer designer, art worker, etc. I also wish to thank all teachers and students who have given creative suggestions. I look forward to hearing from both teachers and students' opinions and valuable suggestions that will help improve the book in next edition.Author3rd Bhadra 2082Preface
ContentGeometry (Working hour 25) 51. Lines and Angle2. Solid ShapesArithmetic (Working hour 60) 511. Number System2. Basic Operations3. Fraction4. Decimal5. PercentageMeasurement (Working hour 35) 1481. Time2. Distance3. Weight4. Capacity5. Perimeter6. Area7. Volume of solidStatistics (Working hour 15) 2191. Bill2. Budget3 Bar GraphAlgebra (Working hour 25) 2511. Algebraic Terms and Expressions2. Like and Unlike Terms3. Algebraic Equation of one Variable
GEOMETRY CHAPTER1Warm Up Test2. Name of the following instruments:(a) (b)................................... ...................................1. Name the following shapes:3. Write the name of the following angles:(a) (b) (c)4. Write the size of the given angles (Use protractor):(a) (b) (c) ....................... ....................... ....................... ....................... ....................... .......................AO BAO BDE FDE FH IGH IG0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 156 5 4 3 2 10 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060.................. .................. .................. .................. ..................1 Line and AngleAcme Mathematics 5 5
5. Write the name of the sides of the given figures.(a) (b) ....................... ....................... .......................AB CCADBSPRQ ....................... ....................... ....................... ....................... ....................... .......................AB CP SQ R6. Write the name of the vertices of the given triangle and quadrilateral:(a) (b) (c)Read the protractor and tick the correct measure.0 180170 10160 2030 150140401305011010080100110706050403020100 180170160150140130120908070120600 180170 10160 2030 150140401305011010080100110706050403020100 180170160150140130120908070120600 180170 10160 2030 150140401305011010080100110706050403020100 180170160150140130120908070120600 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060120° 60° 180° 50° 80° 130° 130° 70° 110° 80° 40° 140° Activity6 Acme Mathematics 5
ActivityStudy the protractor given below.0 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060Z AONow do the following,(a) Draw the angle BOA, where ∠BOA = 34°.(b) Draw the angle AOG where ∠AOG = 85°.(c) Draw the angle AOH where ∠AOH = 136°.(d) Draw the angle AOY where ∠AOY = 165°.(e) Draw the angle AOM where ∠AOM = 185°.(f) Draw the angle AOX where ∠AOX = 120°.RememberYou should start measuring from the side which the base arm is facing.Acme Mathematics 5 7
In the protractor the degrees are : from right to left, 0 to 180°, it is anticlockwise. from left to right, 0 to 180°, it is clockwise.How to measure the angle ?The following activities are the clear ideas to measure the angle. Draw an angle AOB. Put the protractor along OB, such that base line of protractor overlap to OB line. Read the degree that OA overlap the protractor's line1.1 Measurement of an AngleWhat is the measure of ∠AOB? We use protractor to measure the angle.0 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060 Protractor measures the angle in degree Each line indicates 1 degree (°)AO B0 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060AO B60°AO BNote: Put centre of the protector over the vertex of the angle. If base line is toward the right side from center of protractor, use the inside scale.∠AOB = 60°8 Acme Mathematics 5
1.2 Construction of an AngleHow to construct the angle ?Construct an angle of 50°.We use protractor to construct the angle in degree. Draw a base line (arm) AB. Adjust your protractor along the line segment (arm) AB as shown. Mark the point C at 50° from right to left scale. Join the point A and C.Here, ∠BAC = 50°Let ∠ABC is a given angle.Now, Measure the angle ABC. It is 70° Draw a line segment (arm) ON. Adjust your protractor at ON as shown. In the figure and mark at 70°from right to left scale. Remove the protractor and join the points O and M.Here, ∠MON = 70° which is required angle.A B0 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060A BC70°AB C0 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060O NMO NA BC50°O NM70°1.3 Construction of an Angle Equal to the Given AngleAcme Mathematics 5 9
0 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060It is .......... degree.0 180170 10160 2030 150140401305011010080100110706050403020100 180170160150140130120908070120600 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060It is .......... degree. It is .......... degree.0 180170 10160 2030 150140401305011010080100110706050403020100 180170160150140130120908070120600 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060It is .......... degree. It is .......... degree.0 180170 10160 2030 150140401305011010080100110706050403020100 180170160150140130120908070120600 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060It is .......... degree. It is .......... degree.1. Read the following protractors and fill in the blanks.0 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060It is .......... degree.AAAAAAAABB BBBBBBO OOOO OOOClasswork10 Acme Mathematics 5
1. Measure the following angles using protractor:(a) B (b) (c)O A O EDF GO(d) (e) (f)(g) (h) (i)(a) (b) (c)O NMO RPSO TU OVX OY2. Measures the following angles:OZY∠AOB = ....................∠AOC = ....................∠AOC = ....................∠COB = ....................∠AOC = ....................∠BOC = ....................ACOBCA O BBOAC∠AOD = ....................∠BOC = ....................∠AOC = ....................∠BOD = ....................∠AOD = ....................∠COB = .....................(d) (e) (f) ADOBCAO DBCDOBACExercise 1.1Acme Mathematics 5 11
(a) (b) (c)(d) (e) (f)ODA3. Measure the marked angle in angular man given below:4. Construct the following angles using protractor:(a) 20° (b) 40° (c) 60° (d) 80° (e) 100°(f) 125° (g) 178° (h) 180° (i) 22° (j) 27°5. Construct the angle whose measure is same as the angles given below:6. Name and measure the angles from the given figure (List any 10):O BAP QRXY ZAOBFEDBDHGCAF E12 Acme Mathematics 5
Types of angle according to their size(i) Here, ∠AOB = 90°It is right angle.(ii) Here, ∠POQ = 60°It is less than 90°. It is acute angle.O BA90°O QP60°(iii) Here, ∠XOY = 135°It is greater than 90°.It is obtuse angle.(iv) Here, ∠ABC = 180°It is straight angle.O YX135°180°A B C(v) Here, ∠AOB = 220°It is more than 180°. It is reflex angle.(vi) Angle of a complete turn (Exactly 360°).It is called full (complete) turn angle.220°BO A 360°O A1.4 Types of AngleAcme Mathematics 5 13
Solved ExampleExample 1 : Measure the angles and classify them.(a) (b) Solution : (a) Here, ∠AOB = 58°, So, it is an acute angle(b) Here, ∠PQR = 135°, So, it is an obtuse angle.Example 2 : Study the given figure(a) Find the measure of ∠AOC(b) Find the measure of ∠COB(c) Find the measure of ∠AOB(d Are sum of ∠AOC and ∠COB, right angle?Solution : Here,(a) Measure of ∠AOC in 55o.(b) Measure of ∠COB in 35o.(c) Measure of ∠AOB in 90o.(d) As the sum of ∠AOC and ∠COB is a right angle.Example 3 : In the given figure ∠AOC and ∠COB are shown.Solution : Here, by using protector ∠COB = 80°and ∠AOC = 100°Those, size of ∠COB = 80°and size of ∠AOC = 100°OABRP QCOABA O BC14 Acme Mathematics 5
0 180170 10160 2030 150140401305011010080100110706050403020100 180170160150140130120908070120600 180170 10160 2030 150140401305011010080100110706050403020100 18017016015014013012090807012060It is .......... degree.It is .......... degree.It is .......... degree.It is .......... degree.It is ........................ angle.It is ........................ angle.It is ........................ angle.It is ........................ angle.0 180170 10160 2030 150140401305011010080100110706050403020100 180170160150140130120908070120600 180170 10160 2030 150140401305011010080100110706050403020100 180170160150140130120908070120601. Read the protractors and fill in the blanks.an obtuse1402. Classify the marked angles as right, acute or obtuse.ClassworkAcme Mathematics 5 15
16 Acme Mathematics 5
1. Measure and name the following angles:(a) (b) (c) ............................. ........................... ...........................(d) (e) (f) ............................. ........................... ...........................(g) (h) (i) ............................. ........................... ...........................right angle ∠MONacute angle ∠PORstraight angle ∠AOBobtuse angle ∠XOYXO YAO BO RPM O N3. Match the following.Exercise 1.2Acme Mathematics 5 17
2. Observe the given angles, measure them and fill in the blanks.Measure : .............. degreeIt is ......................... angle.Measure : .............. degreeIt is ......................... angle.2. Match the followings:Acute AngleObtuse AngleRight AngleReflex AngleComplete AngleStraight Angle18 Acme Mathematics 5
3. Classify the following angles according to their size:(a) 30° (b) 90° (c) 180° (d) 120° (e) 60°(f) 20° (g) 27° (h) 44° (i) 170° (j) 15°4. Write the differences between right angle and the following angles:(a) 70° (b) 80° (c) 40° (d) 30° (e) 60°5. Write the differences between straight angle and the following angles:(a) 100° (b) 120° (c) 50° (d) 30° (e) 90°Measure : .............. degreeIt is ......................... angle.Measure : .............. degreeIt is ......................... angle.Measure : .............. degreeIt is ......................... angle.Measure : .............. degreeIt is ......................... angle.Measure : .............. degreeIt is ......................... angle.Measure : .............. degreeIt is ......................... angle.Acme Mathematics 5 19
Objective: To know about the size of angle.1. Materials required : A4 size paper, Strips of same size, Scissors, Glue, Different colours.2. Activities:• Cut the strip (juice pipe) in same length.• Paste on A4 size paper making different size angles.• Colour the angle.3. Example:Acute AngleObtuse angle Right angleStraight angle64°180°140° 90°Project Work20 Acme Mathematics 5
1.5 Triangle and Its AnglesIn the figure, AB, BC and CA are 3 line segments. ∠ABC, ∠BCA and ∠CAB are three angles. A, B and C are three corner points ABC is a closed figure.ABC is a triangle. It is a plane closed figure. Triangle is denoted by '∆'(a) All angles less than right angleLook at the given triangle ABC. Measure the angles. Here, ∠BAC = 80°, ∠ABC = 70° and ∠BCA = 30°All angles are acute angles (less than 90°). Triangle ABC is an acute angled triangle.(b) One angle right angleLook at the triangle PQR. Measure the angles.Here, ∠PQR = 90°, ∠QRP = 40° and ∠QPR = 50°.One angle of the triangle PQR is 90°. Triangle PQR is right angled triangle.(c) One angle obtuse angleIn triangle DEF,∠DEF = 110°, ∠EFD = 20° and ∠EDF = 50°One angle of the triangle DEF is obtuse angle (more than 90°). Triangle DEF is an obtuse angled triangle.Check : Sum of angles in all triangles.B CA'∆' is Greek letter 'delta'.AB70°80°30°CPQ R50°90°40°EFD110°50°20°Acme Mathematics 5 21
Classwork1. Fill in the blanks:(a) A triangle has ....................... sides.(b) A triangle has ....................... angles.(c) A triangle has ....................... corners.(d) The measure of ................... is 60°(e) The measure of ................... is 50°(f) The measure of ................... is 70°2. Write 'T' for true sentence and 'F' for false sentence.(a) A triangle has 4 sides.(b) A triangle has 2 sides. (c) A triangle has 3 sides. (d) Small triangle has 2 angles. (e) Big triangle has 3 vertices.(f) Triangle is a closed figure. (g) Triangle is a plane figure. Exercise 1.31. Write the name of the following triangles.(a) (b) (c)B CA50° 70°60°22 Acme Mathematics 5
(d) (e) (f)2. Using protractor measure the size of angles of the following triangles.(a) (b) (c)∠ABC = ...........∠BCA = ...........∠CAB = ...........∠DEF = ...........∠EFD = ...........∠FDE = ...........∠XYZ = ...........∠YZX = ...........∠ZXY = ...........(d) (e) (f)∠ABC = ...........∠BCA = ...........∠CAB = ...........∠XYZ = ...........∠YZX = ...........∠ZXY = ...........∠DEF = ...........∠EFD = ...........∠FDE = ...........(g) (h) (i)AB CDE F Y ZXAB C Y ZX FD EMN OSTRL MNAcme Mathematics 5 23
∠MNO = ...........∠NOM = ...........∠OMN = ...........∠TRS = ...........∠RST = ...........∠STR = ...........∠LMN = ...........∠MNL = ...........∠NLM = ...........3. Measure the angles of the given triangle and complete the table:(a)∠YXZ ∠XYZ ∠YZX ∠YXZ + ∠XYZ + ∠YZX(b)∠BAC ∠ABC ∠BCA ∠BAC + ∠ABC + ∠BCA(c)∠EDF ∠DEF ∠EFD ∠EDF + ∠DEF + ∠EFD4. Check the measure of the following angles, correct the measure if necessary.(a) (b) (c)(d) (e) (f)Y ZXAB CEFD80°40°60°ABC90° 40°40°LM NGH I180°30° 20°70°30°80°PQRX ZY30° 85°40°60°60°90°MNO24 Acme Mathematics 5
5. Measure the angle of the given triangle and find sum:(a)∠ABC∠BCA∠CAB∠ABC + ∠BCA + ∠CABSum of the angles(b)∠DEF∠EFD∠FDA∠DEF + ∠EFD + ∠FDASum of the angles(c)∠GHI∠HIG∠IGH∠GHI + ∠HIG + ∠IGHSum of the angles(d)∠PQR∠QRP∠RPQ∠PQR + ∠QRP + ∠RPQSum of the angles(e)∠OMN∠MNO∠NOM∠OMN + ∠MNO + ∠NOMSum of the anglesAB CDE FGH IOMNP RQAcme Mathematics 5 25
Project Work1. Objective : To find the size of angles in triangles.2. Materials required :A-4 size paper, Scale, A pair of scissors, Glue, Different colours3. Activity: Cut the paper in triangular shape Colour each shape with different colours. Stick (paste) each triangle on A-4 size paper Measure each angles of triangles.4. Example:Observation: Are there all angles of a triangle equal? If yes, you are lucky.60° 70°50°26 Acme Mathematics 5
In the figure, AB, BC, CD and DA are four line segments.∠ABC, ∠BCD, ∠CDA and ∠DAB are four angles.A, B, C and D are four corners (vertices).ABCD is a closed figure.ABCD is a quadrilateral. It is a plane closed figure.Sum of the angles of a quadrilateralABCD is a quadrilateral. Measure the angles ∠ABC, ∠BCD, ∠CDA and ∠DAB. The table below shows the result.∠DAB ∠ABC ∠BCD ∠CDA Sum of angles70° 110° 80° 100° 70° + 110° + 80° + 100° = 360°The sum of all four angles of a quadrilateral is 360°.360° is double of the sum of the angles of a triangle.BD is a diagonal of a quadrilateral ABCD.ABD and BCD are two triangles. The sum of angles of a triangle ABD is 180°.The sum of angles of a triangle BCD is also 180°.Thus,The sum of angles of a quadrilateral ABCD = the sum of angles of a triangle ABD + the sum of angles of a triangle BCD.i.e. Quadrilateral ABCD = ∆ABD + ∆BCDNow,join A and C AC is another diagonal of quadrilateral ABCD. Check the result for ∆ABC and ∆ACD.ADBCDABCDABCDABC1.6 Quadrilateral and Its Interior AnglesAcme Mathematics 5 27
Classwork1. Name the angles of the following quadrilaterals:(a) (b) (c)(d) (e) (f)2. Measure the angles of the following quadrilateral and identify its types(a) (b) (c)∠ABC = ...........It is ......................... .∠BCD = ...........It is ......................... .∠CDA = ...........It is ......................... .∠DAB = ...........It is ......................... .∠SPQ = ...........It is ......................... .∠PQR = ...........It is ......................... .∠QRS = ...........It is ......................... .∠RSP = ...........It is ......................... .∠DMN = ...........It is ......................... .∠MNO = ...........It is ......................... .∠NOD = ...........It is ......................... .∠ODM = ...........It is ......................... .CBAD S RP QDOMN89°Acute angle28 Acme Mathematics 5
Exercise 1.41. Find the angles of the given quadrilateral (use protractor):(a) (b) (c)∠ABC = ...........∠BCD = ...........∠CDA = ...........∠DAB = ...........∠ABC = ...........∠BCD = ...........∠CDA = ...........∠DAB = ...........∠SPQ = ...........∠PQR = ...........∠QRS = ...........∠RSP = ...........2. Check the measure of the angles of the following quadrilaterals and correct if necessary :(a) (b) (c)(d) (e) (f)3. By using protractor find the value of x and y in the following quadrilaterals:(a) (b) (c)DABCAB CD SPQR88°80°64°128°ABCD65°120°80°85°MN OP80° 72°107° 102°CR BT120°72°78° 90°WXYZ96°89°83°92°SARK67°86°110°87°MNOPDx65°75°68°CA BPQS95°80° 80°xREB y D73°88°142°CAcme Mathematics 5 29
(d) (e) (f)4. Measure the angle of the given quadrilateral and find sum. Also measure itssides.(a)∠ABC AB∠BCD BC∠CDA CD∠DAB DAAll angles are different in size.All sides are different in size.It is a quadrilateral only.(b)∠PQR PQ∠QRS QR∠RSP RS∠SPQ SP(c)∠MNO MN∠NOP NO∠OPM OP∠PMN PM110° 115°80°A DyBC120°80°DCA B E100°y100°Q 90°PSR80°xD CBAP SQ RM PN Ox30 Acme Mathematics 5
(d) ∠BCD BC ∠CDE CD ∠DEB DE ∠EBC EB(e)∠ADC AD ∠DCB DC ∠CBA CB ∠BAD BA(f)∠GDE GD ∠DEF DE ∠EFG EF ∠FGD FGBCEDADCBG FD EAcme Mathematics 5 31
1.7 Perpendicular and Parallel LinesJoin the dots and trace the lines.Activity32 Acme Mathematics 5
Study the table and know about the lines.Figure Name ExampleLineLine SegmentRayIntersecting LinesPerpendicular LinesParallel LinesParallel lines are always the same distance apart. They will never meet.Perpendicular lines always cross at right angles.Acme Mathematics 5 33
Join the dots and identify the parallel and perpendicular lines.(a) Parallel and perpendicular line on the gridAPQ R SCBAB and CD are parallel linePR and QS are perpendicular linesD34 Acme Mathematics 5
1. Match the followings.2. Draw parallel lines using real objects. (You can use match box)3. Draw perpendicular lines using real objects. (You can use juice pipe)4. Draw parallel lines on the grid.5. Draw perpendicular lines on the gird.lineintersecting lineperpendicular lineparallel lineExercise 1.5Acme Mathematics 5 35
Warm Up Test1. Name the following shapes:2. Name the vertex:3. Count and write the vertices, faces and edges:4. Paste the picture of the solid shape and name it................... .................. .................. ..................Die Match Box Cone Cylinder SphereVerticesFacesEdges2 Solid Shape36 Acme Mathematics 5
Match the solid shape with their related object.cylinderprismspherecuboidcubeActivity 1Acme Mathematics 5 37
Cube Cuboid Cone Cylinder Sphere2.1 Faces,Vertices and edges of solid shape(a) Shapes around usStudy the given different objects: 38 Acme Mathematics 5
(i) Face (Surface) of the solidOuter part of the solid is called its surface. Surface are also called faces. For example: A cube has six faces or six surfaces.(ii) Vertex of the solidVertex of the solid is corner of it, where three or more than three faces meet.For example: A cube has 8 corners or vertices A, B, C, D, E, F, G and H are the vertices of the cube.(iii) Edges of the solidWhere two faces meet is called the edges of the solid.For example: AB is a edge, where two faces ABCD and ABFE are meet. Similarly; BC, CD, DA, EF, FG, GH, HE, AE, BF, CG and DH are the edges of the given cube.(b) Solid and their propertiesStudy the given informations.ABDGHEFCEdgeVertexFaceEdgeVertexFaceCuboid brick (Cuboid shaped)6 faces12 edges8 verticesCube dice (Cube shaped)6 faces12 edges8 verticesAcme Mathematics 5 39
ConeCylinderSpherePrismBirthday cap (cone shaped)Wooden log (cylinder shaped)Ball (sphere shaped)tent (prism shaped)2 faces1 edge1 vertice3 faces2 edges0 vertices1 face (curved)0 edges0 vertices5 faces (curved)9 edges6 vertices40 Acme Mathematics 5
(c) CubeA cube is the most common solid shape.Dice is a cube. It has six faces. All faces are equal and rectangular. All faces are square in shape.Six faces of dice are given below:Net of the cubeIt is a net of the cube. It has 6 squares. If we fold up, it changes into a cube.Skeleton of a cubeIn the figure alongside Fig. (ii) is the skeleton of fig (i). It is made from the 'juice' pipe and thread. A, B, C, D, E, F, G and H are its vertices. AB, BC, CD, AD, EF, FG, GH, EH, AE, BF, CG and DH are its edges. There are 8 vertices and 12 edges. In the figure, number of pieces of juicepipe are the edges of solid.The cube has: 6 surfaces 8 vertices 12 Edges1 3 6 4251 2 3 4 5 6Dimensions0 1 2 3fig. (i)It is solidE HG FDB CAfig. (ii)SurfaceEdgeVertexAcme Mathematics 5 41
(d) CuboidA cuboid is also a common solid shape. Brick is a cuboid. It has six faces. All faces are not equal. All faces are rectangular in shape.Six faces of brick are given below:Net of the cuboid 1 2 3 4565 2 6143It is a net of the cuboid. It has 6 rectangles. If we fold up, it changes into a cuboid.Skeleton of a cuboidIn the figure alongside Fig. (ii) is the skeleton of fig (i). It is made from the 'juice' pipe and thread. A, B, C, D, E, F, G and H are its vertices. AB, BC, CD, AD, EF, FG, GH, EH, AE, BF, CG and DH are its edges. There are 8 vertices and 12 edges. In the figure, number of pieces of juicepipe are the edges of solid.The cuboid has also 6 surfaces, 8 vertices and 12 Edges.fig. (i)It is solidE HF GDB CAfig. (ii)42 Acme Mathematics 5
1. Circle the correct word that describe each shape.2. Write the number of surfaces, vertices and edges of each figure:No. of Vertex : .............No. of Faces : .............No. of edges : .............No. of Vertex : .............No. of Faces : .............No. of edges : .............No. of Vertex : .............No. of Faces : .............No. of edges : .............sphere prism cone cylindercube sphere cone pyramidcone sphere cylinder prismsphere cone pyramid cubesphere cuboid pyramid cylinder3. Study the given solid shape and fill in the blanks.It has .......... vertices.It has ........ faces.It has ......... edges.Exercise 1.6Acme Mathematics 5 43
1. (a) Study the given shape and fill in the blanks.(b) Name the given angle in 2 ways.i. ....................ii. ....................2. (a) Fill in the blanks.i. .................... is an arm.ii. .................... is a vertex.iii..................... is an arm. (b) Name the angle according to its measure.It is ....................3. (a) Fill in the blanks.i. ............... has six faces.ii. ............... has eight vertices.iii. ............... has twelve edges.(b) Name the real objects which has 6 faces.4. (a) Measure the given angle.It is ....................(b) Define obtuse angle.(c) Draw parallel lines.It has ............... rectangular faces.BAC100°AO BPO RMixed Exercise44 Acme Mathematics 5
5. (a) Define acute angle.(b) Name any four solid shapes around your home.(c) Label the parts of the given solid.6. (a) Define right angle.(b) If ∠BOC = 90°, find the value of x.OxBC20°(c) How many angles should be added to 80° to make it obtuse angle?7. (a) Measure the angles of the given quadrilateral.∠DEF = ..............................∠EFG = ..............................∠FGD = ..............................∠GDE = ..............................(b) Write the types of angle in above figure.8. Using protractor, construct an angle 100°.(a) Name the angle.(b) Write its type.(c) How much more is it from right angle?(d) Draw perpendicular lines.9. Complete the table:∠P ∠Q ∠R ∠P + ∠Q + ∠R10. In the given line segment AB,A B(a) Draw an angle of 90° at point A and B.(b) Construct a parallel line, AB||CD = 5 cm with the help of the angle formed.DGE FPQ RAcme Mathematics 5 45
11. (a) What is quadrilateral? Draw a quadrilateral.(b) How many sides does a quadrilateral have?12. Given figure is ∠ABC(a) Measure ∠ABC using protractor.(b) What type of angle is ∠ABC?(c) Name the arm and vertix of ∠ABC.13. Observe the given figure and write the following:(a) Name the given solid shape.(b) Number of surface.(c) Number of vertices.(d) Number of edges.14. Observe the given figure:(a) How many angles are there in the given figure?(b) Measure the angle ∠QOR by using protractor and write its measure.(c) Find the value of 'a'.(d) Find the measure of ∠POR without measuring by a protractor.15. (a) Draw ∠ABC = 120° by using a protractor.(b) Observe the given solid.i. Name the given solid.ii. Write the number of faces, vertices and edges of the given solid.16. (a) In the diagram, ∠AOB is a straight angle, find the value of x.i. 45° ii. 60°iii. 75° iv. 180°(b) How many types of triangles are there, according to their angles?i. 2 ii. 3 iii. 4 iv. 5(c) Which shape is your classes' white board?i. Cube ii. rectangular iii. cylinder iv. sphere17. (a) Draw the angles 45° using protractor.(b) Find the missing angle of the given triangle. (use protractor)B CAP O QR3aA O B4x70° 50°?46 Acme Mathematics 5
18. Study the given figure and answer the followingquestions.(a) How many angles are formed in the given figure?(b) Find the measure of ∠COB.(c) Find the measure of ∠AOC.19. Look at the triangle and answer the following questions.(a) Write the name of this triangle.(b) How many vertices does it have? Also write their names.(c) Write the name of opposite side of the angle A.20. Study the given figure and answer the following questions.(a) Write the name of two sides in the given figure.(b) Name any two angles.(c) Name any two vertices.21. (a) Find the value of unknown angle.(b) Draw a right angled triangle.(c) Write the number of arms in a triangle.22. Study the given angle and answer the following questions.(a) Which instrument is used to measure an angle?(b) Write two arms of the given angle.(c) Measure and write the value of given angle.23. Study the given figure and answer the following questions.(a) Measure the side AB of the given triangle.(b) Observe and write the smallest angle of the given triangle?(c) Measure any two angles of the given triangle.CA O BB CAB CAA TC40°60° ?PQ RB CAAcme Mathematics 5 47
24. (a) What is right angle?(b) Draw an angle of 90° with the help of protractor.25. Study the given picture and answer the following questions.(a) Write the name of quadrilateral.(b) How many sides and angles are included in the given figure?(c) Write the measurement of angle C with the help of protractor in the given figure.(d) In the given figure, find the value of x?26. Study the figure and fill in the blanks.(a) It has ................ sides.(b) It has ................ vertices.27. Using protractor, construct an angle 100°.(a) Name an angle.(b) Write its type.(c) How much more is it from right angle.28. From the given figure, answer the questions.(a) Name the given figure.(b) What is the sum of interior angles of a quadrilateral?(c) Find the value of x. (use protractor)(d) Write the vertices of given figure.29. From the given figure, answer the following questions.(a) Write the name of the angle which is 90°.(b) Are x° and 55° equal? Give reason.(c) Find the size of angle x. (use protractor)30. (a) Find the unknown angles from the given triangle.B CA(b) Draw an angle of 110° using protractor.AB CDxB CAB55°x°CDAB CDxA48 Acme Mathematics 5
EvaluationTime: 72 minutes Full Marks: 301. (a) Write the names of vertex and arms in the following figure. [1](b) Measure the OB arms by using a scale. [1](c) Draw the 700 angle by using protractor. [2](d) Which is greater angle, 700 and ∠AOB ? By how much ? [2]2. (a) What is an angle less than 900 called? [1] (b) What is the value of x in the given figure? [2](c) Write the measure of ∠ COA. [1](d) Which angle is greater? ∠ COB or ∠ BOA? [1]3. (a) Write the vertex, sides and angle of the following rectangle. [2] (b) How many edges does a cube have? [1] (c) Draw an 800 angle using a protractor. [1] 4. (a) Classify the angle : 1200. [1] (b) Find the unknown angle of quadrilateral. [2] (c) What is the value of 'a' ? [1] AO BABOCx 300WX YZA BD C50o130o80o1300 aaAcme Mathematics 5 49
5. (a) Classify the given angles as acute angle, right angle and obtuse angle. [1]55o, 79o, 170o, 90o (b) Find the unknown angle (x) in the given triangle. [2](c) What type of the triangle is the triangle according to the angle base. [1](d) How many vertices and faces are there on the given box? [1]6. (a) What is the measurement of line segments AB and BC ? Find it by using ruler. [2] (b) Write the line segment parallel to AD. [1] (c) Are line AB and line BC parallel? [1] (d) Draw a line perpendicular to line BC. [2]AB Cx 03 0 0B CA Dx050 Acme Mathematics 5