Answer:
x = 6°
y= 25°
Explanation:
in a cyclic quadrilateral, sum of opposite angles is 180° . So here sum of the angles B and D will be 180° . Similarly sum of angles W and C will be 180° . We can write a equation as ,
ang. W + ang. C = 180
2y + 89 + 8x + 3 = 180
8x + 2y + 92 = 180
8x + 2y = 180 - 82
8x + 2y = 98 . . . . . (1)
Again , we have;
10x - 6 + 2y + 76 = 180
10x + 2y +70 = 180
10x + 2y = 180 - 70
10x + 2y = 110 . . . . . (2)
Subtract equation (1) and (2) to eliminate y,
10x - 8x +2y -2y = 110 - 98
2x = 12
x = 12/2
x = 6
plug this value in equation (1) ,
8*6 + 2y = 98
48 + 2y = 98
2y = 98 - 48
2y = 50
y = 50/2
y = 25
and we are done!