Question

in circle r with ( mangle qrs = 46^{circ} ), find the measure of minor arc ( overarc{qs} ).

Explanation:

Step1: Recall the central angle - arc relationship

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

Step2: Identify the central angle

In circle \(R\), \(\angle QRS\) is the central angle subtended by minor arc \(\overset{\frown}{QS}\). Given \(m\angle QRS = 46^{\circ}\).
Since \(m\overset{\frown}{QS}=m\angle QRS\) (by the central angle - arc relationship in a circle), so \(m\overset{\frown}{QS}=46^{\circ}\).

Answer:

\(46^{\circ}\)