Given angle DEF = (4x + 27) degrees and arc FGD = (16x - 21) degrees, find x and angle DEF.
When a quadrilateral is inscribed in a circle, the sum of the opposite angles is 180 degrees.
∠DEF + ∠FGD = 180
4x + 27 + 16x - 21 = 180
x = 8.7
∠DEF = 4x + 27 = 4*8.7 + 27 = 61.8º
∠FGD = 16x - 21 = 16*8.7 - 21 = 118.2º
