what is m∠egf? write your answer as an integer or decimal. m∠egf =
what is m∠egf? write your answer as an integer or decimal. m∠egf =
Answer
Explanation:
Step1: Find the measure of arc $EF$
The measure of the central - angle is equal to the measure of the intercepted arc. The central - angle $\angle EHF=360^{\circ}-(111^{\circ}+115^{\circ}) = 360^{\circ}-226^{\circ}=134^{\circ}$, so the measure of arc $EF$ is $134^{\circ}$.
Step2: Use the inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc. $\angle EGF$ is an inscribed angle and it intercepts arc $EF$. So $m\angle EGF=\frac{1}{2}\text{ measure of arc }EF$. Since the measure of arc $EF = 134^{\circ}$, then $m\angle EGF=\frac{134^{\circ}}{2}=67^{\circ}$.
Answer:
$67$