measure of angle formed by intersecting chords
Check the final answer first, then review the worked steps.
Problem
measure of angle formed by intersecting chords
Step-by-step solution
The angle formed by two intersecting chords is half the sum of the intercepted arcs. Thus, $\angle RST = \frac{1}{2}(m \stackrel{\frown}{QT} + m \stackrel{\frown}{PR})$. We are given $m \stackrel{\frown}{QT} = 77^\circ$ and $m \stackrel{\frown}{PR} = 47^\circ$. Therefore, $\angle RST = \frac{1}{2}(77^\circ + 47^\circ) = \frac{1}{2}(124^\circ) = 62^\circ$.
Answer
$62^\circ$