When the quadrilateral is inscribed in a circle (a "cyclic" quadrilateral), opposite angles are supplementary. This fact gives a relationship between angles B and D that lets us find the value of x. ∠B + ∠D = 180 (2x-4) + (3x+9) = 180 5x +5 = 180 x = (180 -5)/5 = 35
Now, we can find angle C as ∠C = 180 - ∠A ∠C = 180 - (2×35+3) ∠C = 107°
