Question

the sum of either pair of opposite angles of the cyclic quadrilateral is 180

Answer 1

YESS!! RIGHT!!

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Answer 2

SOLUTION____________________

Refer to the above attachment

Draw OB and OD

Now By the property

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle......

Angle BOD = 2(Angle BAD)

Angle BAD = ½ Angle BOD _______(¹)

Similarly

Angle BCD = ½ Angle BOD ________(²)

On adding both the equations

Angle BAD + Angle BCD = ½ Angle BOD + ½ Angle BOD

Angle BAD + Angle BCD = ½ (Angle BOD + Angle BOD)

Angle BAD + Angle BCD = ½ (360°)

Angle BAD + Angle BCD = 180°

Angle A + Angle C = 180°

Similarly

Angle B + Angle D = 180°