Question

please solve this problem​

Answer 1

Step-by-step explanation:

In triangle PBC

x+y+p =180

Angle p =180 -(x+y)

In triangle ARD

x+y+angle R =180

Angle R =180-(x+y)

Angle P=Angle R

therefore ,PQRS is a parallelogram

AB is parallel to CD

2x+2y is equals to 180

x+y=90

Angle P=180-90=90

therefore, PQRS is a rectangle

Answer 2

Step-by-step explanation:

In ABCD || gm

• AE is bisector of angle A.
• DH is bisector of angle D
• BF is bisector of angle B.
• CG is bisector of angle C.

To prove = JKLI is a rectangle.

In || gm ABCD.

angle ABC + angle BAD = 180°

Angle JAB = 1/2 angle BAD. eq1

(AJ is bisector of angle A.)

Angle JBA = 1/2Angle ABC. eq2

( BJ is bisector of angle B)

Adding eq 1 and 2

Angle ( JAB + JBA ) = 1/2 Angle ( BAD+ ABC)

Angle JAB + angle JBA = 90°

( because 1/2 of adjacent angle of || gm)

In triangle AJB .

angle JAB+ JBA = 90°

So angle AJB = 90°

Interior angle sum property.

Similarly

In triangle DLC

angle DLC = 90°

In Triangle ADI

We get angle AID = 90°

so angle JIL = 90°

(Because angle AID and Angle JIL are vertically opposite angles.)

So 3 angle of a quadrilateral are 90° so 4th will also 90°

Thus JKLI is a rectangle.

Hope it may help you.