By the Inscribed Quadrilateral Theorem, a quadrilateral can only be inscribed if and only if opposite angles are supplementary. This means that [tex]\angle D \text{ and } \angle B[/tex] are supplementary, or add up to 180°. This gives us the equation
(3x + 9)° + (2x - 4)° = 180°
Combine like terms:
5x + 5 = 180
Subtract 5 from each side:
5x + 5 - 5 = 180 - 5
5x = 175
Divide both sides by 5:
5x/5 = 175/5
x = 35
This means that [tex]m \angle D=3(35)+9=114
\\m \angle B=2(35)-4 = 66
\\m \angle A=2(35) + 3=73[/tex]
We take these 3 angles away from 360 and we will have the measure of angle C:
360 - 114 - 66 - 73 = 107°
