Question

prove that the sum of either pair of of opposite angles of a cyclic quadrilateral is 180 degree​

Answer 1

Step-by-step explanation:

Given:ABCD is a cyclic quad. of a circle with centre at o

To prove: BAD+ BCD=180°

ABC+ ADC=180°

chord AB

angle 5 =angle 8(angle in same segment are equal)

chord BC

angle 1 =angle 6(same)

chord CD

angle 2=angle 4(same)

chord AD

angle 7=angle 3(same)

by angle sum property of quad.

A+B+C+D=360°

angle 1+angle 2 +angle 3 +angle 4+ angle 5+ angle 6+ angle 7 +angle 8=360°

(angle1+ angle2+ angle7+ angle8)+(angle3+ angle4+ angle5+ angle6)=360°

2(angle1+ angle2+ angle7+ angle8)=360°

angle1+ angle2+ angle7+ angle8=360°/2

(angle1+ angle2)+(angle 7+ angle8)=180°

BAD+ADC=180°

Similarly,

ABC+ADC=180°

Hence proved.