Question

If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram .

Answer 1

Let the measure of the angle be x

∴ The measure of the angle adjacent is  `(2x)/3`

We know that the adjacent angle of a parallelogram is supplementary

Hence x + `(2x) / 3` = 180°

2x + 3x = 540°

⇒ 5x = 540°

⇒ x = 108°

Adjacent angles are supplementary

⇒ x +108° = 180°

 ⇒ x =180° -108° = 72°

⇒ x = 72°

Hence, four angles are : 180°, 72°,108°, 72°