Final Answer:
B. 53 degrees because The measure of angle PQR is 53 degrees because it complements the right angle formed by the diameter QOR, and PSR is given as 37 degrees.
Step-by-step explanation:
In a circle where (QOR) is a diameter, the angle formed by any point on the circle and the endpoints of the diameter is always a right angle, which means (PQR) is a right angle.
Additionally, (PSR) is given as 37 degrees. Since the sum of angles in a triangle is 180 degrees, and we already have a right angle, we can find (PQR) by subtracting the given angle (PSR) from 90 degrees (the measure of a right angle). Therefore, (PQR) is (90 - 37 = 53) degrees.
In detail, a circle is divided into 360 degrees, and a diameter cuts it into two semicircles, each subtending a 180-degree angle at the center. As (QOR) is a diameter, it forms a straight line and thus measures 180 degrees.
Since (PQR) is formed on this diameter, it must add up to 180 degrees as well. However, we're given that (PSR) is 37 degrees, and since (PQR\) is a right angle, it accounts for 90 degrees.
Subtracting (PSR) from this gives us (PQR)'s measure: \(90 - 37 = 53\) degrees. Therefore, the correct answer is option B, 53 degrees.
Therefore, the correct answer is option b