Question

The opposite angles of a cyclic quadrilateral are x and 3x. What are the measures of the angles of this quadrilateral?

Answer 1

Given: Opposite angles of a cyclic quadrilateral are x and 3x.
Let the angles of the quadrilateral be ∠A, ∠B, ∠C and ∠D.
∠A = 3 × ∠C
But ∠A+ ∠C = 180° (Sum of opposite angles of a cyclic quadrilateral is 180°)
⇒ 4∠C = 180°
⇒ ∠C = 45°
So, ∠C = 45°
and ∠A = 3 ×∠C = 135°