Question

difference between the measures of opposite angles of a cyclic quadrilateral is 12 find the measures of both the angles

Answer 1

We know that sum of the opp angles of a cyclic qua..... is 180 ( degree)
Let x be the measure of one of the angles, then
the measure of the other angle = 180 - x
But it is given that
Difference of the angles = 12
x - (180-x ) = 12
x - 180 + x  = 12
              2x = 12 + 180
                x = 192/2 = 96 ( degree )
Therefore the angles are x and ( 180 - 96)
= 96 and 84 ( degree )

Hope it helped