Question

$\angle$SQR=30${}^{\circ }$, $\angle$QRS=$\angle$PSR=90${}^{\circ }$ and PR=QS.
What is the measure of $\angle$SRP

• A. 30${}^{\circ }$
• B. 40${}^{\circ }$
• C. 50${}^{\circ }$
• D. 60${}^{\circ }$

Answer 1

The correct option is D 60${}^{\circ }$

Consider $△$PSR and $△$QRS
$\angle$QRS=$\angle$PSR=90${}^{\circ }$ (given)
PR=QS (given hypotenuse)
SR = SR ( common side)
$△$PSR$\cong$$△$QRS by RHS criterion for congruency of triangles

So, $\angle$SQR=$\angle$RPS=30${}^{\circ }$

In $△$PSR using angle sum property of triangle.
$\angle$SRP=180${}^{\circ }$-($\angle$PSR+$\angle$RPS)
$⟹$ $\angle$SRP=180${}^{\circ }$-(90${}^{\circ }$+30${}^{\circ }$)
$⟹$ $\angle$SRP=180${}^{\circ }$-120${}^{\circ }$
$⟹$ $\angle$SRP=60${}^{\circ }$