Question

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

a.(6x−4)°+(2x+16)°=180°
b. (x+16)°+(6x−4)°=180°
c. (6x−4)°+(2x+16)°=360°
d. (x+16)°+(6x−4)°=360°

Answer 1

The correct equation to calculate the measure of ∠PQR is (6x-4)°+(2x+16)°=180°, reflecting that opposite angles in a cyclic quadrilateral sum to 180°.

Step-by-step explanation:

To calculate the measure of ∠PQR in quadrilateral OPQR, which is inscribed in circle N, we must consider the properties of inscribed angles and their intercepted arcs in a circle. The sum of the measures of ∠PQR and its opposite angle must equal to 180° because they are inscribed angles that form a pair of opposite angles of a cyclic quadrilateral. Therefore, the correct equation to find the measure of ∠PQR is:

(6x−4)°+(2x+16)°=180°

This is because angles P and R of quadrilateral OPQR add up to 180°, as they subtend the same arc of circle N. This reflects that opposite angles in a cyclic quadrilateral sum to 180°. Answer choice (a) represents this relationship accurately.