Step-by-step explanation:
[tex] m\angle BAD = \frac{1}{2} m(\overset {\frown} {BCD}) ... (1)\\[/tex]
(By inscribed angle theorem)
[tex] m\angle BCD = \frac{1}{2} m(\overset {\frown} {BAD}) ... (2)\\[/tex]
(By inscribed angle theorem)
Adding equations (1) & (2)
[tex] m\angle BAD+m\angle BCD \\= \frac{1}{2} m(\overset {\frown} {BCD}) +\frac{1}{2} m(\overset {\frown} {BAD}) \\\\
= \frac{1}{2} (m\overset {\frown} {BCD} +m\overset {\frown} {BAD}) \\\\
= \frac{1}{2}\times 360°\\\\
= 180°\\\\
\purple {\boxed {\bold {\therefore m\angle BAD+m\angle BCD =180°}}} \\\\
\therefore \angle A \: and \: \angle C \: are \: supplementary\\[/tex]
