Question

Question 4 Multiple Choice Worth 6 points)

Answer 1

Answer:

50°

Step-by-step explanation:

The diagram shows the arc RQ with the measure of 80°, this means the central angle ROQ (where O is the center of the circle) has the same measure of 80°. Angle QPR is inscribed angle subtended on the arc RQ. Its measure is half of the measure of the central angle QOR, so

$m\angle QPR=\dfrac{1}{2}\cdot 80^{\circ}=40^{\circ}$

In right triangle PQR, the sum of two acute angles is 90°, so

$m\angle QPR+m\angle PQR=90^{\circ}\\ \\40^{\circ}+m\angle PQR=90^{\circ}\\ \\m\angle PQR=90^{\circ}-40^{\circ}\\ \\m\angle PQR=50^{\circ}$