Question

In the figure line $AB\parallel$ line $CD$, line $PR$ is the transversal. Ray $PQ$ and ray $RT$ are the angle bisectors of $\angle BPR$ and $\angle PRD$ respectively. They intersect each other in point $S$. Then what is the $m\angle PSR$?

• A. ${30}^{\circ }$
• B. ${90}^{\circ }$
• C. ${60}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B ${90}^{\circ }$

Sum of interior angles x & y is ${180}^o$

on same side of line

$x+y={180}^o$ …………(i)

In triangle PSR sum of angle is ${180}^o$

$\frac{x}{2}+\frac{y}{2}+\angle PSR={180}^o$

$\angle PSR=180-\frac{1}{2}(x+y)$

From (i) $x+y=180$

$\angle PSR={90}^o$.