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°