find the measure of an angle formed by intersecting chords in a circle
Check the final answer first, then review the worked steps.
Problem
find the measure of an angle formed by intersecting chords in a circle
Step-by-step solution
The angle formed by two chords intersecting inside a circle is the average of the measures of the intercepted arcs. Thus, $m\angle RST = \frac{1}{2}(m\text{arc } PT + m\text{arc } QR) = \frac{1}{2}(43^\circ + 131^\circ) = \frac{1}{2}(174^\circ) = 87^\circ$.
Answer
87^\circ