Question

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

Explanation:

Step1: Identify central and inscribed angles

We know that $\angle EDG = 111^\circ$ is a central angle subtending arc $EG$, and $\angle EFG$ is an inscribed angle subtending the same arc $EG$.

Step2: Apply inscribed angle theorem

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

Step3: Calculate the angle

Substitute $m\angle EDG = 111^\circ$ into the formula:
$m\angle EFG = \frac{1}{2} \times 111^\circ = 55.5^\circ$

Answer:

$55.5$