In a cyclic quadrilateral ABCD, if (∠B − ∠D) = 60°, show that the smaller of the two is 60°.

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Solution

In cyclic quadrilateral ABCD, we have:
∠B + ∠D = 180° ...(i) (Opposite angles of a cyclic quadrilateral )
∠B - ∠D = 60° ...(ii) (Given)
From (i) and (ii), we get:
2∠B = 240°
⇒ ∠B = 120°
∴ ∠D = 60°
Hence, the smaller of the two angles is 60°.

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