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. x = 50${}^{\circ }$
• B. y = 77${}^{\circ }$
• C. y = 87${}^{\circ }$
• D. x = 60${}^{\circ }$

Answer 1

Answer: (A), (B)

The correct options are
A

x = 50${}^{\circ }$

B

y = 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${}^{\circ }$