Question

points n, p, and r all lie on circle o. arc pr measures 120°. how does the measure of angle rnq relate to the measure of arc pr? angle rnq is equal in measure to arc pr. angle rnq is half the measure of arc pr. angle rnq is twice the measure of arc pr. angle rnq is four times the measure of arc pr.

Explanation:

Step1: Recall the tangent - secant angle formula

The measure of an angle formed by a tangent and a secant drawn from an external point to a circle is half the difference of the measures of the intercepted arcs. In this case, \(\angle RNQ\) is formed by a tangent \(RQ\) and a secant \(NPQ\). The intercepted arc is \(PR\). The formula for \(\angle RNQ=\frac{1}{2}\text{(measure of arc }PR)\)

Answer:

Angle RNQ is half the measure of arc PR.