Question

In quadrilateral ABCD, angle A = angle C ,angle B = 2 the angle A and angle D = 1/2 the angle A . Find angle A,B,C and D.

Answer 1

$a = c$
$b = 2a$
$d = \frac{1}{2} a$
From the Angle Sum Property of Quadrilaterals,
$a + b + c + d = 360$
$a + b + c + d = 360$
$c + 2c + c + \frac{c}{2} = 360$
$4c + \frac{c}{2 } = 360$
$\frac{8c + c}{2} = 360$
$9c = 360 \times 2$
$c = \frac{720}{9}$
Therefore,
c=80°
a=c=80°
b=2a=2 x 80°=160°
d=c/2=80/2=40°

Answer 2

A=60,B=120,C=60,D=30