what is m∠s? write your answer as an integer or decimal. m∠s = °
what is m∠s? write your answer as an integer or decimal. m∠s = °
Answer
Explanation:
Step1: Find the measure of arc $TU$
The sum of the arcs of a circle is $360^{\circ}$. Given two arcs are $73^{\circ}$ and $82^{\circ}$. Let the measure of arc $TU$ be $x$. Then $x + 73^{\circ}+82^{\circ}=360^{\circ}$. So $x=360^{\circ}-(73^{\circ} + 82^{\circ})=205^{\circ}$.
Step2: Use the inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc. Angle $\angle S$ is an inscribed angle that intercepts arc $TU$. So $m\angle S=\frac{1}{2}\text{ arc }TU$. Since $\text{ arc }TU = 205^{\circ}$, then $m\angle S=\frac{205^{\circ}}{2}=102.5^{\circ}$.
Answer:
$102.5$