Question

Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.

Answer 1

The ratio between two adjacent angles of a || gm ABCD are in the ratio 4 : 5

Let $\angle A=4xand\angle B=5x$

But $\angle A+\angle B={180}^{\circ }$

$\Rightarrow 4x+5x={180}^{\circ }$

$\Rightarrow 9x={180}^{\circ }$

$\therefore x=\frac{{180}^{\circ }}{9}={20}^{\circ }$

$\therefore \angle A=4x=4\times {20}^{\circ }={80}^{\circ }$

$\angle B=5x=5\times 20={100}^{\circ }$