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Question
Two unequal angles of a parallelogram are in the ratio 2 : 3. Find all its angles in degrees .
Solution
Let `∠`A = 2x and `∠`B = 3x
Now,
`∠`A + `∠`B = 180° [Co-interior angles are supplementary]
2x + 3x -180° [ AD || BC and AB is the transversal]
⇒ 5x =180°
⇒ x = `(180°)/ 5` = 36°
∴`∠`A = 2 ´ 36° = 72°
`∠` B = 3´ 36° = 108°
Now,
`∠`A = `∠`C = 72° [Opposite side angles of a parallelogram are equal]
`∠`B = `∠`D =108°
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