Question

what is ( mangle egf )?
write your answer as an integer or decimal.
( mangle egf = square^circ )

Explanation:

Step1: Identify central and inscribed angles

$\angle EHF$ is a central angle with $m\angle EHF=107^\circ$. $\angle EGF$ is an inscribed angle subtending the same arc $\overset{\frown}{EF}$.

Step2: Apply inscribed angle theorem

The measure of an inscribed angle is half the measure of its subtended central angle.
$m\angle EGF = \frac{1}{2}m\angle EHF$

Step3: Calculate the angle measure

$m\angle EGF = \frac{1}{2} \times 107^\circ$

Answer:

$53.5$