MCQ
- A$85^{\circ}$
- B$145^{\circ}$
- C$135^{\circ}$
- D$40^{\circ}$
✓
Answer
A. $85^{\circ}$
Through point $R$ draw $E F\|A B\| C D$.$
\begin{array}{lll}
& \angle A P R=\angle P R F & \text { [Alternate angles] } \\
\Rightarrow & \angle P R F=180^{\circ}-135^{\circ}=45^{\circ} & \\
\text { Also, } & \angle F R Q=\angle CQR & \text { [Alternate angles] } \\
\Rightarrow & \angle F R Q=40^{\circ} &
\end{array}
$
$
\text { Hence, } \angle P R Q=\angle P R F+\angle F R Q=45^{\circ}+40^{\circ}=85^{\circ}
$
Through point $R$ draw $E F\|A B\| C D$.$
\begin{array}{lll}
& \angle A P R=\angle P R F & \text { [Alternate angles] } \\
\Rightarrow & \angle P R F=180^{\circ}-135^{\circ}=45^{\circ} & \\
\text { Also, } & \angle F R Q=\angle CQR & \text { [Alternate angles] } \\
\Rightarrow & \angle F R Q=40^{\circ} &
\end{array}
$
$
\text { Hence, } \angle P R Q=\angle P R F+\angle F R Q=45^{\circ}+40^{\circ}=85^{\circ}
$
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