Question

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

Explanation:

Step1: Identify arc measure

The central angle $\angle HFI = 61^\circ$, so the measure of its intercepted arc $\overset{\frown}{HI}$ is also $61^\circ$.

Step2: Apply inscribed angle theorem

The inscribed angle $\angle HGI$ intercepts arc $\overset{\frown}{HI}$. The inscribed angle is half the measure of its intercepted arc.
$m\angle HGI = \frac{1}{2} \times m\overset{\frown}{HI}$
$m\angle HGI = \frac{1}{2} \times 61^\circ$

Answer:

$30.5$