Vedanta Excel in Mathematics Book - 7 Final (2077)

Geometry: Angles

(iv) Co-interior angles P B
M D
In the figure given alongside, ∠a and ∠d are a pair of ab
interior angles lying to same side of the transversal, A dc
They are called co-interior (consecutive interior) angles.
Similarly, ∠b and ∠c are another pair of co-interior angles. C N
Q
Thus, a pair of interior angles lying on the same
side of transversal are said to be co-interior angles.
Co-interior angles always lie in the ' '-shaped of parallel lines.

The sum of a pair of co-interior angles made by a transversal with parallel
lines is always 180°.

Pairs of angles between parallel lines at a glance Properties
Parts of angles Diagrams

Alternate ∠a = ∠b
angles

Corresponding ∠a = ∠b
angles

Co-interior ∠a+∠b = 180°
angles

Worked-out examples

Example 1: Find the sizes of unknown angles in the following figures.

a) b)

wx 40°
100° y
z x
25°

Solution:

a) (i) w = 100° [Being vertically opposite angles]

(ii) x = w = 100° [Being corresponding angles]

(iii) y = x = 100° [Being vertically opposite angles]

y + z = 180° [Being the sum of a pair of co-interior angles]

or, 100° + z = 180°

or, z = 180° – 100° = 80°

So, w = x = y = 100° and z = 80°

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Geometry: Angles

b) Through the point E, PQ parallel to the given parallel lines AB and CD is drawn.

(i) ∠a = 40° [Being alternate angles] A 40° B
(ii) ∠b = 25° [Being alternate angles]

∠a + ∠b + ∠x =360° [Being part of a complete turn] P ax Q
or, 40°+25° + ∠x = 360 C bE D
or, ∠x = 360° − 65° 25°

∴ ∠x = 295°

EXERCISE 13.2
General Section - Classwork
1. From the given figure, let's tell and write the answers in the blanks spaces.

a) ∠d and ........................... are alternate angles.

b) ∠a and ............................ are corresponding angles. ab
c) ∠c and ............................ are co – interior angles. dc
d) ∠q and ∠d are ...................................... angles.
e) ∠c and ∠m are ...................................... angles. mn
f) ∠d and ∠m are ...................................... angles. qp

2. In each of the following questions, there are four options. Out of which one
option is correct. Let's tick (√ ) the correct option.
a) Which of the following statement is not true?
(i) A pair of alternate angles between parallel lines are equal.
(ii) A pair of corresponding angles between parallel lines are equal.
(iii)A pair of co- interior angles between parallel lines are complementary.
(iv) A pair of co- interior angles between parallel lines are supplementary.

b) In the figure alongside, a pair of corresponding angles is ab
(i) ∠a and ∠c dc
(ii) ∠b and ∠r pq
(iii)∠d and ∠q sr
(iv) ∠p and ∠a

c) In the given figure, which of the following is true? 12
(i) ∠1 = ∠8 43
(ii) ∠4 = ∠5
(iii)∠2 = ∠7 56
(iv) ∠8 = ∠2 87

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Geometry: Angles

d) In the adjoining figure, which of the following is not true? ab
(i) ∠m + ∠x =180° nm
(ii) ∠a + ∠y = 180° pq
(iii) ∠n + ∠p = 180° yx
(iv) ∠a + ∠q = 180°

3. Each of the pair of these angles are formed between parallel lines. Let's tell
and write the answers as quickly as possible.

a) If x° and 45° are a pair of alternate angles, then x° = ......................

b) If a° and 120° are a pair of corresponding angles, then a° = ......................

c) If p° and q° are a pair of co-interior angles, then p° + q° = ......................

d) If x° and 40° are a pair of co-interior angles, then x° = ......................

e) If m° and 150° are a pair of alternate exterior angles, then m° = ......................

Creative Section - A

4. a) What is a transversal? Write with a diagram.

b) Define alternate angles with the help of a diagram.

c) Define corresponding angles with the help of a diagram.
d) Define co-interior angles with the help of a diagram.
e) Write the properties of alternate angles, corresponding angles and co-interior

angles made by a transversal between parallel lines.

5. Let's name the pairs of alternate angles, corresponding angles and co-interior
angles in the following figures.

a) A b) P c) d) C
B
PQ Z YD
BC W
X Y XT A
Q R

6. Let's find the sizes of unknown angles.

a) b) c) p° d) c°

y° b° 60° q° b° d°
x° c° r° a°
40° a°
45° 65°
e°

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Geometry: Angles

e) f) f° g) w° h)

110° w° 105° b° c° 85° y°
z° y° x°
e° 110° x° y° x° 130°
70° a° d° z°

i) c° j) k) l)

145° z° y° c° b° 55°
x° 115°
a° b° a° 150° a°
65° b°

m) n) 100° o) p) w°
w°
y° z° z° a° x° z° 55°
x° 80° x° y° 35°
y° x° y° 65°
25° b°

7. From the given figure, let's find the sizes of unknown angles .

a) b) c) d)

2x° (2x−25)° (3a+25)° (2x+69)° (x+96)°
(2a+5)°
y° x° (x+55)°

Creative Section - B

8. In the given figures, find the measurements of unknown angles.
a) b) c) d)

35° 150° 140° 140°
100°
x° x° y° x°
25° 20° 130°

9. a) In the figure alongside, show that w° x° a° b°
(i) ∠w = ∠c (ii) ∠x = ∠s (iii) ∠y = ∠g z° y° d° c°
(iv) ∠a = ∠r (v) ∠d = ∠q (vi) ∠p = ∠c p° q° e° f°
s° r° h° g°

b) In the adjoining figure, show that, x° y°
∠a + ∠b + ∠c = 2 right angles. a°

b° c°

c) In the given figure, show that ∠a + ∠b + ∠c + ∠d = 360°. y° c° b°

d° a° x°

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Geometry: Angles

d) In the given figure, show that y = 120°. y°
x°
60°

e) In the given figure, show that ∠a + ∠b = ∠c + ∠d b° a°
d°
f) In the figure alongside, find ∠x and ∠y, and
show that BF and CE are parallel to each other. B c°

10. a) In the given figure, AB // DE, ∠BAC = 120° and F E
∠CDE = 150°, find the value of x° A 100°
[Hint: Produce ED to intersect AC at F.]
x° y°
b) From the figure given alongside, find the value of x. 45° C 55°D
[Hint: Through C, draw CZ // DY // BX]
A B
E
120°
FD

150°

CA X
B 3x°

C 90° Y

D 2x°
E

m°

c) In the figure, if m : n = 4 : 5, find the measure of ∠p. p°
n°

It's your time - Project work!

11. a) Let's cut three sets of 3 paper strips from a chart paper. From each set of 3
paper strips make the models of alternate angles ( -shaped), corresponding
angles ( -shaped) and co-interior angles ( -shaped) between two parallel
strips intersected by another strip using glue stick.

b) With the help of a ruler and set squares, let's draw three pairs of parallel lines
separately. Intersect each pair of parallel lines by a transversal. Measure all
angles made by the transversal between each pair of parallel lines with the
help of a protractor. Then explore the relationships between the following
pairs of angles.

(i) Relationship between alternate angles

(ii) Relationship between corresponding angles

(iii) Relationship between co-interior angles

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