Question

45.
The length of an arc of a circle is
equal to the radius. What is the
measure of the inscribed angle of its
supplementary arc ?
​

Answer 1

Answer:

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.