In parallelogram ABCD, AP, DP, BR and CR are the bisectors of their respective angles.If $∠ S P Q = 90 °$ , then the value of $∠ A S B$ is .

45°

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90°

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135°

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75°

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Solution

The correct option is B 90°
Given figure,

Since AP, DP, BR and CR are the bisectors of their respective angles,
PQRS is a rectangle,
Hence,
$∠ S P Q = ∠ R S P = ∠ P Q R = ∠ Q R S = 90 °$
$∠ P S R a n d ∠ A S B$ are vertically opposite angles,
$∠ A S B = ∠ P S R = 90 °$

Hence, the value of $∠ A S B$ is 90°.

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Similar questions

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

(a) 45°

(b) 60°

(c) 90°

(d) 75°

$In the following diagram, the bisectors of interior angles of the parallelogram PQRS en-close a quadrilateral ABCD.$

$Show that: (i) ∠ P S B + ∠ S P B = 90^{\circ} (i i) ∠ P B S = 90^{\circ} (i i i) ∠ A B C = 90^{\circ} (i v) ∠ A D C = 90^{\circ} (v) ∠ A = 90^{\circ} (v i) ABCD is a rectangle Thus, the bisectors of the angles of a parallelogram enclose a rectangle.$

Q. In parallelogram ABCD, AP, DP, BR and CR are the bisectors of their respective angles.

∠ S P Q = 90 °

, then the value of

∠ A S B

is .

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

Q. ABCD is a quadrilateral and AP and DP are bisectors of

∠ A a n d ∠ D

. The value of x is :

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In parallelogram ABCD, AP, DP, BR and CR are the bisectors of their respective angles.If ∠SPQ=90°, then the value of ∠ASB is .

The correct option is B 90°Given figure, Since AP, DP, BR and CR are the bisectors of their respective angles, PQRS is a rectangle, Hence, ∠SPQ=∠RSP=∠PQR=∠QRS=90° ∠PSR and ∠ASB are vertically opposite angles, ∠ASB=∠PSR=90° Hence, the value of ∠ASB is 90°.

In parallelogram ABCD, AP, DP, BR and CR are the bisectors of their respective angles.If $∠ S P Q = 90 °$ , then the value of $∠ A S B$ is .