Page 171 - ICSE Math 7

Example 5: In the adjoining figure AB || CD, find the value of angles
x, y and z. C
A 110°
Solution: AB || CD and EG is a transversal. Therefore, E
∠AEG + ∠CGE = 180° F 80° y x z G
(Interior angles on the same side of a transversal are D
supplementary) B
⇒ 110° + x = 180°

⇒ x = 180° – 110° = 70°
Similarly, ∠BFG + ∠DGF = 180° (AB || CD and FG is a transversal)
⇒ 80° + z = 180°
⇒ z = 180° – 80° = 100°
Also, x + y + z = 180° (Straight angle)

⇒ 70° + y + 100° = 180°
⇒ y = 180° – 170° = 10°

Example 6: In each of the following figures, find whether PQ is parallel to RS or not.
A P R

50°
P C Q A 50° B
(a) (b) C D
40°
130°

R D S Q S
B

Solution: (a) ∠PCD = ∠ACQ (Vertically opposite angles)

⇒ ∠PCD = 50°
∠PCD + ∠CDR = 50° + 130° = 180°
Thus, the interior angles on the same side of the transversal are supplementary.
Hence, PQ is parallel to RS.
(b) ∠CDS = ∠RDB (Vertically opposite angles)

⇒ ∠CDS = 50°
∠ACQ ≠ ∠CDS
Thus, the corresponding angles are not equal. Hence, PQ is not parallel to RS.

EXERCISE 15.2

1. Identify the given pairs of angles as vertically opposite angles, n
corresponding angles, alternate interior angles, alternate exterior 1 2 l
angles, linear pair or co-interior angles. 4 3
(a) ∠4 and ∠8 (b) ∠1 and ∠3 (c) ∠1 and ∠5 5 6 m

(d) ∠4 and ∠5 (e) ∠6 and ∠8 (f) ∠2 and ∠8 8 7
(g) ∠4 and ∠6 (h) ∠7 and ∠8 (i) ∠3 and ∠6

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