Question 1

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

prove it....

Question 2

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

$\: \:$

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

$\: \:$

Construction Join OB & OD

$\: \:$

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

$\: \:$

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

$\: \:$

$\: \:$

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

$\: \:$

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

$\: \:$

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

$\:$

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

$\: \:$

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

$\: \:$

Hope Helps ! :)

Your comment on this question:

Your answer