Question

in a quadrilateral ABCD angle B + angle D =140 degree angle B : angle D = 1:3 and angle A : angle C = 5:6 find all the angles of the quadrilateral.

Answer 1

ang B+ang D=140 degree
1x+3x=140 degree
4x=140 degree
x=140/4=35

ang B=35 dgree
ang D=105 degree

360-140=220 degree

ang A + ang C=220 degree
5x+6x=220 degree
11x=220 degree
x=220/11
 =20

ang A=100
ang B=120

Answer 2

Ratio of angle B and angle D = 1 : 3
Let angle B = x and angle D = 3x

Ratio of angle A and angle C = 5 : 6
Let angle A = 5x and angle C = 6x

But Angle B + angle D = 140°

x + 3x = 140°
4x = 140°
x = 35°


Angle B = x = 1 × 35 = 35°
Angle D = 3x = 3 × 35 = 105°

As the sum of B and D is 140 degrees....therefore, the sum of angles A and C is equal to 220 degrees

5x + 6x = 220  ⇒  x = 20°

angle A = 5×20 = 100 °
angle C = 6 × 20 = 120°