If the measure of arc QR is 100°, what is the measure of angle PQR?

Solution:

Given, the measure of arc QR = 100°

We have to find the measure of angle PQR.

m∠RPQ = (1/2)(mQR)

= (1/2)100°

m∠RPQ = 50°

Triangle PQR is a right triangle, ∠PRQ = 90°

We know that the sum of interior angles of a triangle is always equal to 180°

So, ∠PRQ + ∠PQR + ∠RPQ = 180°

90° + ∠PQR + 50° = 180°

140° + ∠PQR = 180°

∠PQR = 180° - 140°

∠PQR = 40°

Therefore, the measure of ∠PQR is 40°

If the measure of arc QR is 100°, what is the measure of angle PQR?

Summary:

If the measure of arc QR is 100°, the measure of angle PQR is 40°