Question

Sally drew a circle with right triangle PRQ inscribed in it, as shown below: The figure shows a circle with points P, Q, and R on it forming an inscribed triangle. Side PQ is a chord through the center and angle R is a right angle. Arc QR measures 40 degrees. If the measure of arc QR is 40°, what is the measure of angle PQR? 20° 40° 50° 70°

Answer 1

Answer:

The answer is 70 degrees

Answer 2

Answer:

Step-by-step explanation:

Side PQ is a chord through the center and angle R is a right angle. This means that side PQ is the diameter of the circle.

Let O represent the center of the circle.

If the measure of arc QR is 40°, it means that the central angle formed by arc QR is 40°. Side OR and side OQ are equal because they are both radius of the circle. Therefore, ∆QOR is an isosceles triangle and the base angles are equal.

Therefore, ∠PQR = ∠ORQ

Since the sum of the angles in a triangle is 180°, then

∠PQR = (180 - 40)/2 = 140/2

∠PQR = 70°