Question

Given: A circle with inscribed quadrilateral ABCD

Prove: A and C are supplementary

"Question: 2. By inscribed angle theorem, mA=
Anwser choices a/2, a , 2a

Answer 1

Explanation:

`m\angle BAD = (1)/(2) m(\overset {\frown} {BCD}) ... (1)\\`

(By inscribed angle theorem)

`m\angle BCD = (1)/(2) m(\overset {\frown} {BAD}) ... (2)\\`

(By inscribed angle theorem)

Adding equations (1) & (2)

`m\angle BAD+m\angle BCD \\= (1)/(2) m(\overset {\frown} {BCD}) +(1)/(2) m(\overset {\frown} {BAD}) \\\\</p><p>= (1)/(2) (m\overset {\frown} {BCD} +m\overset {\frown} {BAD}) \\\\</p><p>= (1)/(2)* 360°\\\\</p><p>= 180°\\\\</p><p>\purple {\boxed {\bold {\therefore m\angle BAD+m\angle BCD =180°}}} \\\\</p><p>\therefore \angle A \: and \: \angle C \: are \: supplementary\\`