In parallelogram ABCD, AR and DP are the angle bisectors of angles A and D respectively.If $∠ A D S = 45 °$ , then the value of $∠ P S R$ is .

90°

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

45°

No worries! We‘ve got your back. Try BYJU‘S free classes today!

135°

No worries! We‘ve got your back. Try BYJU‘S free classes today!

75°

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A 90°
Given figure,

$∠ A D S = 45 °$
Co - interior angles are supplementary, and AR and DP are angle bisectors,
$∠ A + ∠ D = 180 °$
$⟹ ∠ A D S + ∠ D A S = 90 °$
Hence, $∠ D S A = 90 °$ (Angle sum property of $△ A S D$ )
$∠ P S R a n d ∠ D S A$ are vertically opposite angles,
$∴ ∠ D S A = ∠ P S R = 90 °$

Hence, the value of $∠ P S R$ is 90°.

Suggest Corrections

Similar questions

In the given figure, ABCD is a parallelogram in which $∠ B D C = 45^{\circ} a n d ∠ B A D = 75^{\circ}$ . Then, $∠ C B D =$ ?

(a) $45^{\circ}$

(b) $55^{\circ}$

(d) $75^{\circ}$

ABCD is a parallelogram, M is the mid-point of BD and BM bisects $∠ B$ . Then $∠ A M B =$

∠ A D S = 45 °

∠ P S R

∠ S P Q = 90 °

∠ A S B

∠ A

∠ D

∠ A O D

45^{\circ}

Join BYJU'S Learning Program