Question

Given: quadrilateral ABCD inscribed in a circle Prove: ∠A and ∠C are supplementary, ∠B and ∠D are supplementary

Answer 1

Answer:

Step-by-step explanation:

Given that quadrilateral ABCD inscribed in a circle

We have angle A and C are lying on either side of the centre.

If O is the centre, we get

AOC will be 2A (as per subtended arc theorem)

Similarly AOC major arc would be 2C

Since 2A+2C = 360(angle around a point)

dividing by 2, we get A+C =180

Or A and C are supplementary

Similarly we can prove B and D are supplementary.