Question

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

Explanation:

Step1: Recall central angle theorem

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

Step2: Identify the central angle and arc

In circle \( R \), \( \angle QRS \) is a central angle that intercepts arc \( \overset{\frown}{QS} \).

Step3: Apply the theorem

Since the measure of arc \( \overset{\frown}{QS} = 34^\circ \), by the central angle theorem, \( m\angle QRS \) is equal to the measure of arc \( \overset{\frown}{QS} \).

Answer:

\( 34^\circ \)