what is m∠rst? write your answer as an integer or decimal. m∠rst = °
what is m∠rst? write your answer as an integer or decimal. m∠rst = °
Answer
Explanation:
Step1: Find the central - angle corresponding to arc RT
The sum of the central - angles in a circle is 360°. Let the central - angle corresponding to arc RT be $\angle{RUT}$. $\angle{RUT}=360^{\circ}-114^{\circ}-137^{\circ}=109^{\circ}$
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. $\angle{RST}=\frac{1}{2}\angle{RUT}$ Since $\angle{RUT} = 109^{\circ}$, then $\angle{RST}=\frac{109^{\circ}}{2}=54.5^{\circ}$
Answer:
$54.5$