what is m∠rts? write your answer as an integer or decimal. m∠rts = °
what is m∠rts? write your answer as an integer or decimal. m∠rts = °
Answer
Explanation:
Step1: Find the central - angle corresponding to arc RS
The sum of angles around a point is 360°. The central - angle $\angle RUS=360^{\circ}-(109^{\circ} + 108^{\circ})=360^{\circ}-217^{\circ}=143^{\circ}$.
Step2: Use the inscribed - angle theorem
The measure of an inscribed angle is half the measure of the central angle subtended by the same arc. Here, $\angle RTS$ is an inscribed angle and $\angle RUS$ is the central angle subtended by arc $RS$. So, $m\angle RTS=\frac{1}{2}m\angle RUS$.
Step3: Calculate the measure of $\angle RTS$
$m\angle RTS=\frac{1}{2}\times143^{\circ}=71.5^{\circ}$
Answer:
$71.5$