Question

In a quadrilateral ABCD, sideAD is parallel to side BC if angle A:angle B =2:3and angle C: angle D=4:5,find each angle of quadrilateral ABCD

Answer 1

firstly, A:B= 2:3

let measure of angles be X.

measure of angle a = 2x

measure of angle b = 3x.

A.T.Q.

2x+3x=180 (co-interior angles)

5x= 180

x=180/5

x=36

measure of angle a = 2x= 2*36= 72.

measure of angle b = 3x = 3*36= 108

now, C:D= 4:5

let measure of angles be X.

measure of angle C = 4x

measure of angle D = 5x.

A.T.Q.

4x+5x=180 (co-interior angles)

9x= 180

x=180/9

x=20

measure of angle C = 2x= 4*20= 80.

measure of angle b = 5x = 5*20= 100

Ans= Measure of angle A = 36, B= 108, C= 80 and D= 100.