what is m∠gfh? write your answer as an integer or decimal. m∠gfh = °
what is m∠gfh? write your answer as an integer or decimal. m∠gfh = °
Answer
Explanation:
Step1: Find the central - angle of arc $GH$
The measure of the central - angle of arc $GH$ is $\angle GEH$. We know that the sum of angles around a point is $360^{\circ}$. So, $\angle GEH=360^{\circ}-(145^{\circ} + 82^{\circ})=360^{\circ}-227^{\circ}=133^{\circ}$.
Step2: Use the inscribed - angle theorem
The inscribed - angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc's central angle. $\angle GFH$ is an inscribed angle and the central angle of the arc it intercepts is $\angle GEH$. So, $m\angle GFH=\frac{1}{2}\angle GEH$. Since $\angle GEH = 133^{\circ}$, then $m\angle GFH=\frac{133^{\circ}}{2}=66.5^{\circ}$.
Answer:
$66.5$