Question

In the figure ,find the four angles A,B,Cand D of the parallelogram ABCD

Answer 1

HERE IS YOURS SOLUTION;

◆ Consider ∆ BDC;

Angle BDC + Angle DCB + Angle CBD = 180° 【Angle Sum Property】

=> 3x + 2x + 5x = 180°

=> 10x = 180°

=> x = 18°

Now, putting the value of x in those angles;

● 5x = 5 × 18 = 90° = Angle C

● 3x = 3 × 18 = 54°

● 2x = 2 × 18 = 36°

Now, consider parallelogram ABCD;

Angle A = Angle C 【Opposite Sides Of A Parallelogram Are Equal】

=> 90° = Angle A

AND;

BD is diagonal of the parallelogram & diagonal of a parallelogram bisects the angles.

● 54° × 2 = 108° = Angle B

● 36° × 2 = 72° = Angle D

◆ So, all the angles of the parallelogram are 90°, 108°, 72°, 90° ◆

HOPE IT HELPS