Question

in the circle below, chords \\( \overline{pq} \\) and \\( \overline{rs} \\) are parallel.

what is \\( m \angle s \\)?
a. \\( 40^\circ \\)
b. \\( 50^\circ \\)
c. \\( 80^\circ \\)
d. \\( 140^\circ \\)

Explanation:

Step1: Use the property of parallel chords and alternate - interior angles

Since chords \(PQ\) and \(RS\) are parallel, \(\angle Q=\angle S\) (alternate - interior angles).

Step2: Recall the property of angles in a circle

In a circle, the measure of an inscribed angle is given. Here, \(\angle Q = 40^{\circ}\) (given).

Answer:

\(40^{\circ}\)