Question -
Answer -
It is given that ∠A – ∠C = 60° and ABCD is a cyclic quadrilateral.
We have to prove that smaller of two is 60°
Since ABCD is a cyclic quadrilateral
So ∠A + ∠C = 180° (Sum of opposite pair of angles of cyclic quadrilateral is 180°) ..… (1)
And,
∠A – ∠C = 60° (Given) ..… (2)
Adding equation (1) and (2) we have
So, ∠C = 60°
Hence, smaller of two is 60°.