Question

In a cyclic quadrilteral abcd ,if angle a-anglec=60 degree ,prove that the smaller of two is60 degree

Answer 1

In the cyclic quadrilateral,
angleA + angleC = 180 degrees .......[i]
also ,
angleA - angleC = 60 degrees
=> angleC = angleA - 60 degrees .........[ii]

Putting [ii] in [i] ,

angleA + angleA - 60 degrees = 180 degrees
=> 2(angleA) = 240 degrees
=> angleA = 120 degrees

From [ii] ,
angleC = 120-60 = 60 degrees.
Therefore, the smaller of the two angles is 60 degrees.