Question

what is ( mangle g )?( mangle g = square^circ )

Explanation:

Step1: Identify inscribed angle property

Angles subtended by same arc are equal. $\angle G$ and $\angle HIG$ subtend arc $HG$.

Step2: Recognize right triangle angle

Since $IG$ is a diameter, $\angle IHG = 90^\circ$ (angle inscribed in semicircle).

Step3: Calculate $\angle G$

In $\triangle IHG$, sum of angles is $180^\circ$.
$$m\angle G = 180^\circ - 90^\circ - 33^\circ$$
$$m\angle G = 57^\circ$$

Answer:

$57$