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The sum of either pair of opposite angle...

The sum of either pair of opposite angles of a cyclic quadrilateral is `180^0` OR The opposite angles of a cyclic quadrilateral are supplementary.

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The opposite angles of a cyclic quadrilaterals are supplimentary

The sum of either pair of opposite angles of a cyclic quadrilateral is 180^(@) OR The opposite angles of a cyclic quadrilateral are supplementary.

Theorem 10.11 : The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

Prove that the sum of opposite pair of angles of a cyclic quadrilateral is 180^(@)

Definition of Cyclic quadrilateral

ABCD is a cyclic quadrilateral (see Figure). Find the angles of the cyclic quadrilateral.

If the sum of any pair of opposite angles of a quadrilateral is 180^(@) ; then the quadrilateral is cyclic.

Theorem 10.12 : If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.