Question

Is bisector of angle A and Angle B of a quadrilateral ABCD intersect each other at P of Angle B and angle C at Q of angle C and angles d at our and of Angle B and Angle A and S then pqrs is a rectangle rhombus parallelogram quadrilateral whose opposite sides are supplementary​

Answer 1

Answer:

hope it will be a great help

Answer 2

Given:

In quadrilateral ABCD, AS, BQ, CQ and DS are

angle bisectors of angles A, B, C and D, respectively.

∠QPS=∠APB

(Vertically opposite angles)

...(1)

In ∆APB,

APB+∠PAB+∠ABP=180∘

(Angle sum property of triangle.)

⇒ angle APB+1/2∠A+1/2∠B=180∘

⇒ angle APB=180∘–1/2(∠A+∠B)

...(2)

From (1) and (2), we get

angle QPS=180∘–1/2(∠A+∠B)

Similarly,

angle QRS=180∘–1/2(∠C+∠D)

...(3)

...(4)

From (3) and (4), we get

angleQPS+∠QRS=360∘–1/2(∠A+∠B+∠C+∠D

=360∘–1/2(360∘

= 360∘–180∘

=180∘

So, PQRS is a quadrilateral whose opposite angles are supplementary.

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