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Question
If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.
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Solution
Let `square`ABCD be the parallelogram.
The ratio of measures of two adjacent angles of a parallelogram is 1 : 2.
Let the common multiple be x.
∴ ∠A = x° and ∠B = 2x°
∠A + ∠B = 180° ...[Adjacent angles of a parallelogram are supplementary]
∴ x + 2x = 180
∴ 3x = 180
∴ x = `180/3`
∴ x = 60
∠A = x° = 60°
∠B = 2x°
= 2 × 60° = 120°
∠A = ∠C = 60°
∠B = ∠D= 120° ...[Opposite angles of a parallelogram]
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