Question

the pairs of opposite angles of a cyclic quadrilateral are supplementary​

Answer 1

$<b>Given</b>$ : A cyclic quadrilateral ABCD

$<b>To Prove</b>$ :

∠A + ∠C = 180°

∠B + ∠D =180°

$<b>Proof</b>$ :

∠D = ½ ∠y .....(1)

∠B = ½ ∠x ......(2)

$<b>By adding (1) and (2)</b>$

∠D + ∠B = ½ (∠y +∠x)

∠B + ∠D = ½ × 360°

$<b>∠B + ∠D = 180°</b>$

similarly,

$<b>∠A + ∠C = 180°</b>$

Answer 2

$\huge\bold{Answer}$

$<b>$

__________________❤Rythm

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°

THANKS !!

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