Question

In the fig. below, if $AB\parallel CD,\angle APQ={50}^{\circ }$ 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

$\because AB\parallel CD$

$\angle APQ=\angle PQR$

$\text{(Alternate interior angles of transversal PQ)}$

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

$\Rightarrow \angle APR=\angle PRD$

$\text{(Alternate interior angles of transversal PR)}$

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

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

$={77}^{\circ }$