Question

The sum of either pair of opposite angles of a cyclic quadrilateral is180°
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Answer 1

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$\huge\bold{Solution}$

Theorem 7 : The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180°. ( Angles are supplementary) .

Given: Let ABCD be a cyclic quadrilateral

To Proof: The sum of either pair of the opposite angles of a cyclic quadrilateral, is 180°. ( Angles are supplementary) .

Given: Let ABCD be a cyclic quadrilateral

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

Construction: Join OB and OD.

Proof :

∠ BOD = 2 ∠BAD

∠ BAD = ∠BOD

similarly , ∠ BCD = ∠DOB

. . ∠ BAD + ∠BCD = ∠ BOD + ∠ DOB

= ( ∠ BOD + ∠DOB)

= × 360°

= 180°

Similarly ∠B + ∠ D = 180°

Hope it helps you out✔✔

Answer 2

Answer:

Step-by-step explanation:

We know that the sum of all angles of a quadrilateral is 360°

Let, abcd be a cyclic quadrilateral.

Then

A+B+C+D=360°

NOW,Join OB and OD.

Proof :

∠ BOD = 2 ∠BAD

∠ BAD = ∠BOD

similarly , ∠ BCD = ∠DOB

therefore ∠ BAD + ∠BCD = ∠ BOD + ∠ DOB

= ( ∠ BOD + ∠DOB)

= × 360°

= 180°

Similarly ∠B + ∠ D = 180°