Question

in circle r with the measure of arc \\( \overarc{qs}=34^{\circ} \\), find \\( m\angle qrs \\).

Explanation:

Step1: Recall the central - angle theorem

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

Step2: Identify the central angle and the intercepted arc

In circle \(R\), \(\angle QRS\) is a central angle and \(\overset{\frown}{QS}\) is its intercepted arc.
Since the measure of arc \(\overset{\frown}{QS} = 34^{\circ}\), by the central - angle theorem \(m\angle QRS=m\overset{\frown}{QS}\)

So \(m\angle QRS = 34^{\circ}\)

Answer:

\(34^{\circ}\)