Question

Prove : Opposite angles of a cyclic quadrilateral are supplementary​

Answer 1

Answer:

Follow me and thanx my answers..

Answer 2

Prove the opposite angles of a cyclic quadrilateral are supplementary.

Step-by-step explanation:

Given : A cyclic quadrilateral ABCD.

To Prove :

angle A + angle C = 180°

angle B + angle D = 180°

Construction : Let O be the center of the circle. Join O to B and D. Then let the angle subtended by the minor arc and the major arc at the centre be x° and y° tespectively.

Proof : x° = 2 angle C ( angle at the centre theorem) ------ eqn 1

y° =2 angle A ------- eqn 2

Adding eqn 1 and 2 we get

x° + y° = 2 angle C + 2 angle A ------- eqn 3

But x° + y° = 360°

From eqn 3 and 4 we get,

2 angle C + 2 angle A = 360°

=> angle C + angle A = 180°

But we know that angle sum property of quadrilateral.

angleA + angle B + angle C + angle S = 360°

angle B + angle D + 180° = 360°

angle B + angle D = 360° - 180°

angle B + angle D = 180°

Hence proved.