Question

In a cyclic quadrilateral two adjacent angles are 40° and `pi^"c"/3`. Find the angles of the quadrilateral in degrees.

Answer 1

Let ABCD be the cyclic quadrilateral such that ∠A = 40° and ∠B = `pi^"c"/3`

= `(pi/3 xx 180/pi)^circ     ...[because theta^"c"  = (theta xx 180/pi)^circ]`

= 60°

∠A  + ∠C = 180°     ...`[("Opposite angles of a cyclic"),("quadrilateral are supplementary")]`

∴ 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°.