Question

in circle r with m∠qrs = 46°, find the measure of minor arc \\(\stackrel\frown{qs}\\).

Explanation:

Step1: Recall central angle - arc relationship

The measure of a minor arc is equal to the measure of its central angle. Here, \(\angle QRS\) is a central angle (since \(R\) is the center and \(Q, S\) are on the circle), so the measure of arc \(\widehat{QS}\) equals \(m\angle QRS\).

Step2: Substitute the given angle measure

Given \(m\angle QRS = 46^\circ\), so the measure of minor arc \(\widehat{QS}\) is also \(46^\circ\).

Answer:

\(46^\circ\)