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Question
Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.
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Solution
Let ABCD be a quadrilateral.
So, ∠A = ∠C
∠B = ∠D
And ∠A + ∠C = 180°, ∠B + ∠D = 180°
Now, ∠A + ∠A = 180° ...[∠C = ∠A]
⇒ 2∠A = 180°
⇒ ∠A = 90°
Similarly, ∠B = 90°
Hence, each angle is a right angle.
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