If an angle of a parallelogram is two-third of its adjacent angle,

Question:

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

Solution:

Let the measure of the angle be x.

Therefore, 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°, 180°, 72°

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