Question

The opposite angle of a cyclic quadrilateral are supplementary.Prove it

Answer 1

Answer:

Step-by-step explanation:

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

Hope it helps

Answer 2

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 (Fig.)

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 (Fig.)

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°

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