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°