what is m∠hgi? write your answer as an integer or decimal. m∠hgi =

Answer:

$60.5$

Explanation:

Step1: Find the central - angle of arc $HI$

The sum of angles around a point is $360^{\circ}$. Let the central - angle of arc $HI$ be $\angle HFI$. So, $\angle HFI=360^{\circ}-(123^{\circ}+118^{\circ})=360^{\circ}-241^{\circ}=119^{\circ}$.

Step2: Use the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc's central angle. $\angle HGI$ is an inscribed angle and $\angle HFI$ is the central angle intercepting the same arc $HI$. So, $m\angle HGI=\frac{1}{2}m\angle HFI$.

Step3: Calculate $m\angle HGI$

$m\angle HGI=\frac{1}{2}\times119^{\circ}=60.5^{\circ}$.