Question

how can we prove that adjacent angles of cyclic quadrilateral is supplementary?​

Answer 1

Answer:

the sum of opposite angle of a cyclic quadrilateral is supplementry not adjacent

Step-by-step explanation:

in the given circle

angle 1 = angle 4 ( angles made by same chord )

angle 2 = angle 6

angle 3 = angle 7

angle 5 = angle 8

we know that sum of angles of a quadrilateral = 360

so

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

angle 1 + angle 2 + angle 7 + angle 1 + angle 8 + angle 2 + angle 7 + angle 8 = 360

now

2* angle 1 + 2*angle 2 + 2* angle 7+

2*angle 8 = 360

2( angle 1 + angle 2 + angle 7 + angle 8 ) = 360

angle 1 + angle 2 + angle 7 + angle 8 = 180

angle A + angle D= 180