Question

in circle p with ( mangle npq = 92^{circ} ), find the measure of minor arc ( overarc{nq} ).

Explanation:

Step1: Recall the central - angle and arc relationship

The measure of a minor arc is equal to the measure of its central angle.

Step2: Identify the central angle

In circle \(P\), \(\angle NPQ\) is the central angle for minor arc \(\overset{\frown}{NQ}\). Given \(m\angle NPQ = 92^{\circ}\).
Since the measure of a minor arc \(\overset{\frown}{NQ}\) is equal to the measure of its central angle \(\angle NPQ\), we have \(m\overset{\frown}{NQ}=m\angle NPQ\).

Answer:

92°