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

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.

Step2: Identify central and inscribed angles

The central angle $\angle EDF = 149^{\circ}$, and the inscribed angle $\angle EGF$ subtends the same arc $\overset{\frown}{EF}$.

Step3: Calculate the measure of $\angle EGF$

By the inscribed - angle theorem, $m\angle EGF=\frac{1}{2}m\angle EDF$. So $m\angle EGF=\frac{1}{2}\times149^{\circ}=74.5^{\circ}$.

Answer:

$74.5$