Question

The sum of either pair of opposite angles of a cyclic quadrilateral is 180 degree..

prove it....​

Answer 1

Given :

• Let ABCD Is Cyclic Quadrilateral

To Prove :

`\gray{ \frak{ \angle A + \angle C = 180° }}`

`\: \:`

`\gray{\frak{\angle B + \angle D = 180°}}`

`\: \:`

Construction Join OB & OD

Proof :

`\: \:`

`\gray{ \frak {\angle BOD = 2 \angle BAD}}`

`\: \:`

`\gray{\frak{ \angle BAD = (1)/(2) \angle BOD}}`

`\: \:`

Similarly :

`\: \:`

`\gray{\frak{\angle BCD = (1)/(2) \angle DOB }}`

`\: \:`

`\gray{\frak{ \angle BAD + \angle BCD = (1)/(2)\angle BOD + (1)/(2) \angle DOB }}`

`\: \:`

`\gray{ \frak { = (1)/(2) ( \angle BOD + \angle DOB )}}`

`\:`

`\gray {\frak{ = ( (1)/(2)) * 360 \degree = 180 \degree }}`

`\: \:`

`\sf similary : \boxed{\color{skyblue}{ \frak{ \angle \: B + \angle D = 180°}}}`

`\: \:`

Hope Helps ! :)