Sally drew a circle with right triangle PRQ inscribed in it, as shown below:

Question

If the measure of arc QR is 40°, what is the measure of angle PQR?

Answer 1

Angle QPR is an inscribed angle that subtends arc QR. The measure of an inscribed angle is equal to one-half of the measure of the arc it subtends, So m∠QPR = (1/2)·40° = 20°. Now you know two of the three angles in triangle PRQ, 90° and 20°. The missing angle is m∠PQR, but we know that all three angles must add to 180° in a triangle:

m∠PQR + 90° + 20° = 180°

Solve for the m∠PQR.