In a cyclic quadrilateral if show that the smaller of the two is 60°.

Question

In a cyclic quadrilateral if show that the smaller of the two is 60&#xB0;.

Philoid · Accepted Answer

Given, ∠B - ∠D = 60°____________________ (i)

ABCD is a cyclic quadrilateral,

∴ ∠B + ∠D = 180°____________________ (ii)

From equation (i) and (ii),

2 ∠B = 240°

⇒ ∠B = 120°________________ (iii)

From equation (ii),

∠B + ∠D = 180°

⇒ 120° + ∠D = 180°[From equation (iii)]

⇒ ∠D = 60°

Hence, the smaller of the two angle ∠D = 60°.