Question

In parallelogram ABCD, AR and DP are the angle bisectors of angles A and D respectively.If $\angle ADS=45°$, then the value of $\angle PSR$ is .

• A. 90°
• B. 45°
• C. 135°
• D. 75°

Answer 1

The correct option is A 90°

Given figure,

$\angle ADS=45°$
Co - interior angles are supplementary, and AR and DP are angle bisectors,
$\angle A+\angle D=180°$
$⟹\angle ADS+\angle DAS=90°$
Hence, $\angle DSA=90°$ (Angle sum property of $△ASD$)
$\angle PSRand\angle DSA$ are vertically opposite angles,
$\therefore \angle DSA=\angle PSR=90°$

Hence, the value of $\angle PSR$ is 90°.