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Question
One pair of the opposite angles of a cyclic quadrilateral is congruent. Write the measures of these angles.
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Solution
Given: Opposite angles of a cyclic quadrilateral are equal.
Let the angles of the quadrilateral be ∠A, ∠B, ∠C and ∠D.
So,∠A = ∠C
But ∠A + ∠C = 180° (Sum of opposite angles of a cyclic quadrilateral is 180°)
⇒ 2∠A = 180°
⇒ ∠A = 90°
So, ∠C = ∠A = 90°
Let the angles of the quadrilateral be ∠A, ∠B, ∠C and ∠D.
So,∠A = ∠C
But ∠A + ∠C = 180° (Sum of opposite angles of a cyclic quadrilateral is 180°)
⇒ 2∠A = 180°
⇒ ∠A = 90°
So, ∠C = ∠A = 90°
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