# Prove that The sum of either pair of opposite angles of a cyclicquadrilateral is 180º.

Hi!
Here is the proof of the statement provided by you.

Consider a cyclic quadrilateral ABCD inscribed a circle with centre at O
In order to prove this theorem, join OB and OD ⇒∠BAD + ∠BCD = 180$°$ ... (1)

Similarly, by joining OA and OC it can be proved that
∠ABC + ∠ADC = 180$°$ ... (2)

Equation (1) and equation (2) shows that the sum of opposite angles of a cyclic quadrilateral is 180 degree.

Cheers!

• 84

The opposite angles of a cyclic quadrilateral are supplementary.

##### Proof Consider a circle, with centre O. Draw a cyclic quadrilateral . Draw and .

The aim is to prove that and . • -4

The opposite angles of a cyclic quadrilateral are supplementary.

##### Proof Consider a circle, with centre O. Draw a cyclic quadrilateral . Draw and .

The aim is to prove that and . • -5 .....

• -4

all you  guys are right..thanks!!!:)

• -6

thank u very much for ur effort Ishan Goyal, it benefitted me a lot!

• 1

by reason

⇒BAD + BCD = 180� ... (1) Similarly, by joining OA and OC it can be proved that ABC + ADC = 180� ... (2) Equation (1) and equation (2) shows that the sum of opposite angles of a cyclic quadrilateral is 180 degree. Hope! This will help you.
• -5

Theorem: The sum of either pair of apposite angles of a cyclic quadrilateral is 180. OR The opposite angles of a cyclic quadrilateral are supplementry. Since PQRS is a cyclic quadrilateral. PSR + PQR - 180 120 + PQR = 180PQR = 60 Since PRQ is the angle in a semi-circle.PRQ = 90 Now, in PQR, we haveQPR + PRQ + PQR = 180QPR+ 90+ 60 = 180QPR = 30PLEASE THUMBS UP

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