Question

Using the exterior angle property, find the value of $y$ from the figure.

• A. ${80}^{\circ }$
• B. ${100}^{\circ }$
• C. ${20}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is B ${100}^{\circ }$


$\angle APQ=\angle PQR$
[Alternate angles are equal]
$\Rightarrow {50}^{\circ }=\angle PQR$

By exterior angle property,
$\Rightarrow \angle PQR+\angle QPR=\angle PRD$
$\Rightarrow {50}^{\circ }+y={150}^{\circ }$
$\Rightarrow y={150}^{\circ }-{50}^{\circ }={100}^{\circ }$
$\Rightarrow y={100}^{\circ }$