Question

If one angle of a parallelogram is twice of its adjacent angle, find the angles of the parallelogram.

Answer 1

Let the two adjacent angles be x and 2 x

In a parallelgram, sum of the adjacent angles are ${180}^{\circ }$

$\therefore x+2x={180}^{\circ }$

$\Rightarrow 3x={180}^{\circ }$

$\Rightarrow x={60}^{\circ }$

Thus, the two adjacent angles are ${120}^{\circ }\text{and}{60}^{\circ }.$

Opposite angles in a parallelogram are equal.

Hence, the angles of the parallelogram are ${120}^{\circ },{60}^{\circ },{120}^{\circ }\text{and}{60}^{\circ }.$