Question

If $ABCD$ is a square where $AP\neg BQ=CR,$ $\angle PQR={90}^{\circ }.$ Based on the above data answer the following questions.
Angle $QPB=?$

• A. ${60}^{\circ }$
• B. ${45}^{\circ }$
• C. ${30}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

$\because \Delta PBQ\cong \Delta RCQ$

hence, their corresponding angles are also equal.

$\therefore \angle PQB=\angle RCQ={45}^{\circ }$

$\therefore \angle CRQ=90-{45}^{\circ }={45}^{\circ }$

$\therefore \angle x=90-\angle CRQ={45}^{\circ }$