Question

In 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. ${77}^{\circ },{97}^{\circ }$

• A. ,
• B. ,
• C. ,
• D. ,

Answer 1

The correct option is B (${50}^{\circ },{77}^{\circ }$)

Since $AB||CD$
So, the alternate interior angles of transversal $PQ$ are equal
$\Rightarrow \angle APQ=\angle PQR$
$\Rightarrow x={50}^{\circ }$
$\angle APR=\angle PRD$
(Alternate interior angles of transversal $PR$)
$y+{50}^{\circ }={127}^{\circ }$
$y={127}^{\circ }$ - ${50}^{\circ }$
$\therefore y={77}^{\circ }$