Question

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

Answer 1

Answer:

$m \angle PQR=80^{\circ}$

Step-by-step explanation:

Missing figure drawn.

The measure of ∠PQR is found by the property of inscribed quadrilateral. In an inscribed quadrilateral the opposite angles are supplementary:

$\left\{\begin{matrix}\angle O+\angle Q=180^{\circ} & \\ \angle P +\angle R=180^{\circ} & \end{matrix}\right.$

$x+16+6x-4=180^{\circ}\\7x+12=180\\7x+12-12=180-12\\7x=168\\\frac{7x}{7}=\frac{168}{7}\\x=14\\\angle Q=6(14)-4\Rightarrow m\angle Q=84-4\Rightarrow Q=80^{\circ}$