To find the measurement of the inscribed angle \( \angle QSR \) given the central angle \( \angle QOR \), we can use the relationship between central angles and inscribed angles.
The measure of an inscribed angle is half the measure of the central angle that intercepts the same arc. Thus, we can express this relationship mathematically as:
\[ \text{Measure of } \angle QSR = \frac{1}{2} \text{Measure of } \angle QOR \]
Given that \( \angle QOR = 107^\circ \), we can substitute this value into the equation:
\[ \text{Measure of } \angle QSR = \frac{1}{2} \times 107^\circ = \frac{107}{2}^\circ = 53.5^\circ \]
So, the measurement of \( \angle QSR \) is \( 53.5^\circ \).
1 answer