# Theorem : Opposite Angles of a Cyclic Quadrilateral are Supplementary | Class 8

Theorem : Opposite Angles of a Cyclic Quadrilateral are Supplementary.

Solution :

Given: ABCD is a cyclic quadrilateral.

R.T.P.(Require To Prove)

1. � + � = 180^{0}

2. � + � = 180^{0}

Construction : Join OB and OD

Proof:

1. ∠ BOD = 2 ∠BAD || Angle at the centre of a circle is twice the angle at the circumference.

2. Reflex ∠ BOD + ∠ BOD = 2 (� + �) || Same as stated above.

or 2 (� + �) = 360^{0} || By statement 2.

or (� + �) = 180^{0}

3. Similarly by joining OA and OC it can be proved that

� + � = 180^{0}

4. ∴ � + � = 180^{0}

& � + � = 180^{0} Proved