what is m∠hgi? write your answer as an integer or decimal. m∠hgi = °
what is m∠hgi? write your answer as an integer or decimal. m∠hgi = °
Answer
Explanation:
Step1: Recall inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc. The central angle $\angle HIJ = 147^{\circ}$, and the inscribed angle $\angle HGI$ intercepts the same arc $\overset{\frown}{HI}$.
Step2: Calculate the measure of $\angle HGI$
By the inscribed - angle theorem, $m\angle HGI=\frac{1}{2}m\angle HIJ$. Since $m\angle HIJ = 147^{\circ}$, then $m\angle HGI=\frac{147}{2}=73.5^{\circ}$.
Answer:
$73.5$