Question

27. The adjacent angles of a Parallelogram have equal measure. Find the measure of each of
the angles of the Parallelogram.​

Answer 1

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The adjacent angles of a Parallelogram have equal measure. Find the measure of each of  the angles of the Parallelogram.​

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Let ABCD be the parallelogram with ∠A = ∠B.

We know: Sum of adjacent angles = 180°

∠A + ∠B = 180º

2∠A = 180º (∠A = ∠B)

∠A = 90º

∠B = ∠A = 90º

∠C = ∠A = 90º (Opposite angles)

∠D = ∠B = 90º (Opposite angles)  

Thus, each angle of the parallelogram measures 90º.

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Answer 2

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Let ABCD be the parallelogram with ∠A = ∠B.

We know: Sum of adjacent angles = 180°

∠A + ∠B = 180º

2∠A = 180º (∠A = ∠B)

∠A = 90º

∠B = ∠A = 90º

∠C = ∠A = 90º (Opposite angles)

∠D = ∠B = 90º (Opposite angles)

. ° . each angle of the parallelogram measures 90º.

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