In a Quadrilateral ABCD, AB is parallel to DC If Angle A : Angle D = 2:3 and Angle - Maths -

Question

In a Quadrilateral ABCD, AB is parallel to DC If Angle A :
Angle D = 2:3 and Angle B ; Angle C = 7:8, find the measure of each
angle

Chetna Khanna · Accepted Answer

Given, AB || DC âˆ A : âˆ D = 2 : 3 âˆ B : âˆ C = 7 : 8 âˆ´ âˆ A = 2x and âˆ B = 7y âˆ D = 3x âˆ C = 8y As AB || DC âˆ´ âˆ A + âˆ D = 180Â° (Linear pair of angles) $\Rightarrow 2 x + 3 x = 180 ° \Rightarrow 5 x = 180 ° \Rightarrow x = \frac{180 °}{5} \Rightarrow x = 36 °$ Also, âˆ B + âˆ C = 180Â° (Linear pair of angles) $\Rightarrow 7 y + 8 y = 180 ° \Rightarrow 15 y = 180 ° \Rightarrow y = \frac{180 °}{15} \Rightarrow y = 12 ° Thus, ∠ A = 2 x = 2 \times 36 ° = 72 ° ∠ B = 7 y = 7 \times 12 ° = 84 ° ∠ C = 8 y = 8 \times 12 ° = 96 ° ∠ D = 3 x = 3 \times 36 ° = 108 °$

In a Quadrilateral ABCD, AB is parallel to DC. If Angle A : Angle D = 2:3 and Angle B ; Angle C = 7:8, find the measure of each angle.