ABCD is a quadrilateral inscribed in a circle, as shown below: Circle O is shown with a quadrilateral ABCD inscribed inside it.
Angle A is labeled x plus 16. Angle B is labeled x degrees. Angle C is labeled 6x minus 4. Angle D is labeled 2x plus 16. What equation can be used to solve for angle C? (x + 16) + (x) = 180 (x + 16) + (6x − 4) = 180 (x + 16) − (2x + 16) = 180 (x + 16) + (x) = 90
The Cyclic Quadrilateral Theorem states that for a quadrilateral in a circle, the opposite angles will equal 180 degrees. So therefore you can conclude:
∠A + ∠C = 180° which would be (x + 16) + (6x - 4) = 180°
