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^o, 67^o
• B. 50^o, 77^o
• C. 77^o, 87^o
• D. 77^o, 97^o

Answer 1

The correct option is B

50^o, 77^o

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${}^{\circ }$