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Answer:
Step-by-step explanation:Given: quadrilateral ABCD is a cyclic quadrilateral.
To Proove: angle B+angle D =180° angle A +angle C =180°
Proof: Arc ABC is intercepted by the inscribed angle ADC.
Therefore angle ADC=1/2 angle ADC..............(1)
Similarly,angle ABC is an inscribed angle .It intercepts arc ADC.
Therefore angle ABC=1/2m(arcADC)........(2)
Therefore measure angle ADC+angleABC =1/2 m(arcABC)+1/2 m(arcADC).........from (1) &(2)
=1/2[ m(arc ABC)+m(arcADC)]
=1/2×360°...arc ABC and arc ADC constitutes a complete circle.
=180°
Similarly we can prove,angle A +angle C = 180°.