Question

In a cyclic quadrilateral two adjacent angles are 40 and π^c/3. Find the angles of the quadralateral in degrees.

Answer 1

Let ABCD be the cyclic quadrilateral such that ∠A = 40° and

= 60°

∴  ∠A + ∠C = 180° 

∴ 40° + ∠C = 180° 

∴ ∠C= 180°- 40°

= 140° Also, ∠B + ∠D = 180°

… [Opposite angles of a cyclic quadrilateral are supplementary] 

∴ 60° + ∠D =180° 

∴ ∠D = 180°- 60° = 120° 

∴ The angles of the quadrilateral in degrees are 40°, 60°, 140° and 120°.