Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠ROP?

Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x plus 16. Angle P is not labeled. Angle Q is labeled 6x minus 4. Angle R is labeled 2x plus 16.
(6x − 4)° + (2x + 16)° = 360° (x + 16)° + (6x − 4)° = 360° (6x − 4)° + (2x + 16)° = 180° (x + 16)° + (6x − 4)° = 180

Question

Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠ROP?

Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x plus 16. Angle P is not labeled. Angle Q is labeled 6x minus 4. Angle R is labeled 2x plus 16.
 (6x − 4)° + (2x + 16)° = 360° (x + 16)° + (6x − 4)° = 360° (6x − 4)° + (2x + 16)° = 180° (x + 16)° + (6x − 4)° = 180

welshfella · Answer

Hint: the opposite angles of a cyclic quadrilateral add up to 180 degrees