Question

In the fig. below, if AB || CD,
$\angle$APQ = 50${}^{\circ }$ and $\angle$PRD = 127${}^{\circ }$, find x and y.

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• A. 50${}^{\circ }$, 67${}^{\circ }$
• B. 50${}^{\circ }$, 77${}^{\circ }$
• C. 77${}^{\circ }$, 87${}^{\circ }$
• D. 77${}^{\circ }$, 97${}^{\circ }$

Answer 1

The correct option is B

50${}^{\circ }$, 77${}^{\circ }$

Since AB || CD,

∠APQ = ∠PQR (Alternate interior angles of transversal PQ)

⇒ x = 50${}^{\circ }$

∠APR = ∠PRD (Alternate interior angles of transversal PR)

⇒ y + 50${}^{\circ }$ = 127${}^{\circ }$

⇒ y = 127${}^{\circ }$ - 50${}^{\circ }$

= 77${}^{\circ }$