**Proof: **

arc ABC is intercepted by the inscribed angle ∠ADC.

∴ ∠ADC m(arcABC) (i) [Inscribed angle theorem]

Similarly, ∠ABC is an inscribed angle. It intercepts arc ADC.

∴ ABC = 1/2 m(arc ADC) (ii) [Inscribed angle theorem]

∴ ∠ADC + ∠ABC

= 1/2 m(arcABC) + 1/2 m(arc ADC) [Adding (i) and (ii)]

∴ ∠D + ∠B = 1/2 m(areABC) + m(arc ADC)]

∴ ∠B + ∠D = 1/2 × 360° [arc ABC and arc ADC constitute a complete circle] = 180°

∴ ∠B + ∠D = 180°

Similarly we can prove,

∠A + ∠C = 180°