Question

prove that the sum of either pair of opposite angles of a cyclic quadrilateral is supplementary​

Answer 1

here are the pics of your proof

Answer 2

Given : a cyclic quadrilateral ABCD

To prove : Angle A +Angle C =180° and angle B + angle D =180°

construction : join AC and BD

proof :. angle ACB =angle ADC (angles in the same segment )

angle BAC = angle BDC. ( angles in the same segment )

Angle ACB + angle BAC = angle ADC + Angle BDC

Angle ACB + angle BAC = angle BDC

Angel ACB + angle BAC + angle ABC = angle BDC + angle ABC ( adding Angle ABC to both the sides )

Angle ABC + angle BDC = 180°

angle B + angle D =180°

angle A + angle B + angle C + angle D = 360°

angle A + angle C = 360 -(angle B + angle D)

angle A + Angle C= 360-180

angle A + angle C =180°

Hence proved