Question

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

Explanation:

Step1: Find $\angle EHF$

The sum of angles around a point is $360^\circ$.
$$m\angle EHF = 360^\circ - 125^\circ - 126^\circ = 109^\circ$$

Step2: Relate central to inscribed angle

The inscribed angle is half the central angle subtended by the same arc $\overset{\frown}{EF}$.
$$m\angle EGF = \frac{1}{2}m\angle EHF$$

Step3: Calculate final angle

Substitute the value of $\angle EHF$.
$$m\angle EGF = \frac{1}{2} \times 109^\circ = 54.5^\circ$$

Answer:

$54.5$