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