Answer:
x = 53 , ∠ D = 135°
Explanation:
ABCD is a cyclic quadrilateral ( its 4 vertices lie on the circle )
the opposite angles are supplementary , sum to 180° , then
∠ A + ∠ C = 180° , that is
2x + x + 21 = 180
3x + 21 = 180 ( subtract 21 from both sides )
3x = 159 ( divide both sides by 3 )
x = 53
so ∠ B = x - 8 = 53 - 8 = 45° , and
∠ D + ∠ B = 180°
∠ D + 45° = 180° ( subtract 45° from both sides )
∠ D = 135°