Given :
- Let ABCD Is Cyclic Quadrilateral
To Prove :
[tex] \gray{ \frak{ \angle A + \angle C = 180° }}[/tex]
[tex] \: \: [/tex]
[tex] \gray{\frak{\angle B + \angle D = 180°}}[/tex]
[tex] \: \: [/tex]
Construction Join OB & OD
Proof :
[tex] \: \: [/tex]
[tex] \gray{ \frak {\angle BOD = 2 \angle BAD}}[/tex]
[tex] \: \: [/tex]
[tex]\gray{\frak{ \angle BAD = \frac{1}{2} \angle BOD}}[/tex]
[tex] \: \: [/tex]
Similarly :
[tex] \: \: [/tex]
[tex]\gray{\frak{\angle BCD = \frac{1}{2} \angle DOB }}[/tex]
[tex] \: \: [/tex]
[tex]\gray{\frak{ \angle BAD + \angle BCD = \frac{1}{2}\angle BOD + \frac{1}{2} \angle DOB }}[/tex]
[tex] \: \: [/tex]
[tex] \gray{ \frak { = \frac{1}{2} ( \angle BOD + \angle DOB )}}[/tex]
[tex] \: [/tex]
[tex] \gray {\frak{ = ( \frac{1}{2}) \times 360 \degree = 180 \degree }}[/tex]
[tex] \: \: [/tex]
[tex] \sf similary : \boxed{\color{skyblue}{ \frak{ \angle \: B + \angle D = 180°}}}[/tex]
[tex] \: \: [/tex]
Hope Helps ! :)
