Question

find the measure of the smaller angle

Answer 1

D : A = 2: 1
D/A = 2/1
D = 2A ......(1)
A = B ......(2)
C = B - 20. ..(3)


A + B+C+D =360°
B + B + B - 20 + 2× A = 360°. 【 from eq. 1,2 and 3】
3B -20 + 2 B = 360°
5B - 20 =360°
5B = 380°
B = 76°

A = B = 76°
D = 2A
= 2 ×76
= 152°
C = B -20
= 76 - 20
= 56


•• HENCE , Angle C is the smallest