The measure of angle PQR is 65°. The last option (65°) is the correct option.
The complete question that shows the diagram is attached below.
From the question, we are to determine the measure of angle PQR.
Angle PQR (<PQR) is one of the angles in the inscribed triangle PRQ.
Consider ΔPRQ
<PRQ = 90° (Angle in a semicircle is 90°)
In order to determine <PQR, we will first determine the measure of <QPR
From the question,
The measure of arc QR is 50°, that means, the angle subtended by arc QR at the center of the circle is 50°.
Let the center of the circle be O
That means, <QOR = 50°
Now,
From one of the circle theorems which states
"Angle at the center is twice that at the circumference"
Then,
<QOR = 2 × <QPR
∴ 50° = 2 × <QPR
<QPR = 50° ÷ 2
∴ <QPR = 25°
Now, consider ΔPRQ
<PQR+ <QPR + <PRQ = 180° (Sum of angles in a triangle)
<PQR + 25° + 90° = 180°
<PQR + 115° = 180°
<PQR = 180° - 115°
<PQR = 65°
Hence, the measure of angle PQR is 65°
Learn more here: brainly.com/question/2286720