what is m∠stu? write your answer as an integer or decimal. m∠stu = °
what is m∠stu? write your answer as an integer or decimal. m∠stu = °
Answer
Explanation:
Step1: Recall inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc.
Step2: Find the measure of the arc $\overset{\frown}{SU}$
The sum of the central - angles around a point is $360^{\circ}$. Let the central - angle corresponding to arc $\overset{\frown}{SU}$ be $x$. Then $x + 114^{\circ}+138^{\circ}=360^{\circ}$. Solving for $x$: [ \begin{align*} x&=360^{\circ}-(114^{\circ} + 138^{\circ})\ x&=360^{\circ}-252^{\circ}\ x& = 108^{\circ} \end{align*} ]
Step3: Calculate the measure of $\angle STU$
Since $\angle STU$ is an inscribed angle and the arc it intercepts is $\overset{\frown}{SU}$, by the inscribed - angle theorem, $m\angle STU=\frac{1}{2}m\overset{\frown}{SU}$. So $m\angle STU=\frac{1}{2}\times108^{\circ}=54^{\circ}$
Answer:
$54$