Question

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio $2:4:5:7.$ Find the measure of each angle of the quadrilateral.

Answer 1

We have $\angle A:\angle B:\angle C:\angle D=2:4:5:7$ So, Let $\angle A=2x^{\circ },\angle B=4x^{\circ },\angle C=5x^{\circ },\angle D=7x^{\circ }.$
$\therefore \angle A+\angle B+\angle C+\angle D={360}^{\circ }$
$\Rightarrow 2x+4x+5x+7x={360}^{\circ }$
$\Rightarrow 18x={360}^{\circ }$
$\Rightarrow x={20}^{\circ }$
Thus, the angles are :
$\angle A=2\times {20}^{\circ }={40}^{\circ },\angle B=4\times {20}^{\circ }={80}^{\circ },$
$\angle C=5\times {20}^{\circ }={100}^{\circ }$
and, $\angle D=7x^{\circ }=7\times {20}^{\circ }={140}^{\circ }$