Question

Prove that sum of either pair of cyclic quadrilateral is 180

Answer 1

$\huge{Answer :}$


$\bold{Given :}$ Let ABCD is cyclic quadrilateral.

$\bold{To\: prove :}$ ∠A + ∠C = 180° and ∠B + ∠D = 180°.

$\bold{Construction :}$ Join OB and OD.

$\bold{Proof :}$ ∠BOD = 2 ∠BAD

∠BAD = 1/2∠ BOD

Similarly ∠BCD = 1/2 ∠DOB

∠BAD + ∠BCD = 1/2∠BOD + 1/2 ∠DOB

=½(∠ BOD + ∠DOB)

= (½)X360° = 180°
$<b>$
Similarly ∠B + ∠D = 180°

Answer 2

Answer:

Step-by-step explanation:

Given : A cyclic quadrilateral ABCD

To prove :

< A (angle A) + < C (angle C) = 180

< B (angle B) + < D (angle D) = 180

Proof : <D + <B = 1/2 <y + 1/2 <x

<D + <B = 1/2 (<y + <x)

<B + <D = 1/2 (360)

<B + <D = 180

Similarly <A + <C = 180