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Charra [1.4K]
3 years ago
15

Question 4 Multiple Choice Worth 6 points)

Mathematics
1 answer:
Kryger [21]3 years ago
3 0

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}

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