Intersecting Chords (Finding Angle Measure)

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle .

In the figure,

$m\angle 1=\frac{1}{2}\left(m\stackrel{⌢}{QR}+m\stackrel{⌢}{PS}\right)$ .