Question

Two adjacent angles of a parallelogram are as 1:2 Find the measure of all the angles of the parallelogram.

Answer 1

Let in parallelogram ABCD,

$\angle A:\angle B=1:2$
Let $\angle A=x$, then $\angle B=2x$
But $\angle A+\angle B={180}^{\circ }$
(Sum of adjacent angles)
$\Rightarrow x+2x={180}^{\circ }\Rightarrow 3x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }}{3}={60}^{\circ }$
$\therefore \angle C=\angle A$ and $\angle D=\angle B$
(Opposite angles)
$\therefore \angle C={60}^{\circ }$ and $\angle D={120}^{\circ }$
Hence $\angle A={60}^{\circ },\angle B={120}^{\circ },\angle C={60}^{\circ }$ and $\angle D={120}^{\circ }$