In a cyclic quadrilateral ABCD, if (∠B − ∠D) = 60°

Question:

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

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:
2B  = 240°
⇒ B = 120°
∴ ∠D = 60°
Hence, the smaller of the two angles is 60°.

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