By the Inscribed Quadrilateral Theorem, a quadrilateral can only be inscribed if and only if opposite angles are supplementary. This means that

are supplementary, or add up to 180°. This gives us the equation
(3
x + 9)° + (2
x - 4)° = 180°
Combine like terms:
5
x + 5 = 180
Subtract 5 from each side:
5
x + 5 - 5 = 180 - 5
5
x = 175
Divide both sides by 5:
5
x/5 = 175/5
x = 35
This means that

We take these 3 angles away from 360 and we will have the measure of angle C:
360 - 114 - 66 - 73 = 107°