Question

In a cyclic quadrilateral ABCD, if ∠A − ∠C = 60°, prove that the smaller of two is 60°

 

 

Answer 1

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

${\displaystyle 2\angle A=240°}$

     ${\displaystyle \angle A=\frac{240°}{2}}$

            = 120°

So, ∠C = 60°

Hence, smaller of two is 60°.