Question 19

In the given figure, PQ|| SR and SP|| RQ. Then, angles a and b are respectively

(a) $20^{\circ}, 50^{\circ}$
(b) $50^{\circ}, 20^{\circ}$
(c) $30^{\circ}, 50^{\circ}$
(d) $45^{\circ}, 35^{\circ}$

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Solution

Given PQ || SR and PR is transversal.
$∴ ∠ Q P R = ∠ S R P [a l t e r n a t e i n t e r n a t e a n g l e s] \Rightarrow a = 20^{\circ}$
Also SP|| RQ and PR is transversal.
$∴ ∠ S P R = ∠ Q R P [a l t e r n a t e i n t e r n a t e a n g l e s] \Rightarrow b = 50^{\circ}$

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Question 19 In the given figure, PQ|| SR and SP|| RQ. Then, angles a and b are respectively (a) 20∘,50∘ (b) 50∘,20∘ (c) 30∘,50∘ (d) 45∘,35∘

Given PQ || SR and PR is transversal. ∴∠QPR=∠SRP [alternate internate angles]⇒a=20∘ Also SP|| RQ and PR is transversal. ∴∠SPR=∠QRP [alternate internate angles]⇒b=50∘

Question 19

In the given figure, PQ|| SR and SP|| RQ. Then, angles a and b are respectively

(a) $20^{\circ}, 50^{\circ}$
(b) $50^{\circ}, 20^{\circ}$
(c) $30^{\circ}, 50^{\circ}$
(d) $45^{\circ}, 35^{\circ}$

Given PQ || SR and PR is transversal.
$∴ ∠ Q P R = ∠ S R P [a l t e r n a t e i n t e r n a t e a n g l e s] \Rightarrow a = 20^{\circ}$
Also SP|| RQ and PR is transversal.
$∴ ∠ S P R = ∠ Q R P [a l t e r n a t e i n t e r n a t e a n g l e s] \Rightarrow b = 50^{\circ}$