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Question
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
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Solution
Let ABCD be a parallelogram, in which, let m∠A = m∠B = x
Since sum of two adjacent angles is 180°
∠A + ∠B = 180º
x + x = 180°
2x = 180°
x = 90º
∠C = ∠A = 90º (Opposite angles)
∠D = ∠B = 90º (Opposite angles)
Thus, each angle of the parallelogram measures 90º.
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