Question

Prove that, the opposite angles of a cyclic quadrilateral are supplimentery​

Answer 1

given: quadrilateral ABCD IS cyclic

to prove: angle B + angle D = 180

proof: arc ABC is intercepted by the inscribed angle ADC

angle ADC =1/2 m ( arc ABC)..........1

SIMILARLY , angle ABC is an inscribed angle. it intercepts arc ADC

angle ABC =1/2m( arc ADC)..........2

m angle ADC+m angle ABC=1/2 arc ABC+1/2 m arc ADC ...(1 and 2)

=1/2 m arc ABC + m arc ADC

=1/2×360....(arc ABC and arc ADC constitute a complete circle)

=180°