Question

$PQRS$ is a rhombus with $\angle PQR={54}^{\circ }$. Determine $\angle PRS$

• A. $\angle PRS={53}^{\circ }$
• B. $\angle PRS={63}^{\circ }$
• C. $\angle PRS={73}^{\circ }$
• D. $\angle PRS={83}^{\circ }$

Answer 1

Answer: (B)

$\angle PRS={63}^{\circ }$

Given that $PQRS$ is a rhombus

$\angle PSR=\angle PQR={54}^{\circ }$ (opp. $\angle S$ of a rhombus are equal)

$\Rightarrow \angle OSR=\frac{1}{2}\times \angle PSR=\frac{1}{2}\times {54}^{\circ }={27}^{\circ }$ ($SQ$ bisects $\angle PSR$)

Now in $\Delta OSR$

$\angle ORS+\angle ROS+\angle OSR={180}^{\circ }$

$\Rightarrow \angle ORS+{27}^{\circ }+{90}^{\circ }={180}^{\circ }$

(Diagonals of a rhombus bisect each other at right $\angle s$)

$\Rightarrow \angle ORS={63}^{\circ }$

$\Rightarrow \angle PRS={63}^{\circ }$