Question

the sum of a pair of opposite angles of a quadrilateral is 180 degree the quadrilateral is cyclic. tell the theorem

Answer 1

this is the property of a cyclic quadraliteral. you can find it on 9th standard maths books in chapter 8 quadraliterals

Answer 2

Theorem 10.12

Sol :-

Given : Let ABCD is cyclic quadrilateral.

To prove : ∠A + ∠C = 180° and ∠B + ∠D = 180°.

Construction :-join OB and OD.

Proof : ∠BOD = 2 ∠BAD
∠BAD = 1/2∠ BOD
Similarly ∠BCD = 1/2 ∠DOB
∠BAD + ∠BCD = 1/2∠BOD + 1/2 ∠DOB
=1/2(∠ BOD + ∠DOB)
= (1/2)X360° = 180°
Similarly ∠B + ∠D = 180°.