Question

In the figure, sides $QP$ and $RQ$ of $△PQR$ are produced to points $S$ and $T,$ respectively. If $\angle SPR={135}^{\circ }$ and $\angle PQT={110}^{\circ }$, find $\angle PRQ.$

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

From figure,

${110}^{\circ }+\angle 2={180}^{\circ }$ [since, $RQT$ is a straight line]

$\Rightarrow \angle 2={180}^{\circ }-{110}^{\circ }$

$\Rightarrow \angle 2={70}^{\circ }$

Also, $\angle 1+{135}^{\circ }={180}^{\circ }$ [since, $QPS$ is a straight line]

$\Rightarrow \angle 1={180}^{\circ }-{135}^{\circ }={45}^{\circ }$

Also, $\angle 1+\angle 2+\angle R={180}^{\circ }$ [angle sum property of triangle]

$\Rightarrow {45}^{\circ }+{70}^{\circ }+\angle R={180}^{\circ }$

$\Rightarrow \angle R={180}^{\circ }-{115}^{\circ }={65}^{\circ }$

Therefore, $\angle PRQ=65°$

Hence, Option D is correct.