Question

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Explanation:

Step1: Identify right angle property

Since $GF$ is the diameter, $\angle GEF = 90^\circ$ (angle inscribed in a semicircle is a right angle).

Step2: Sum triangle angles to 180°

The sum of angles in $\triangle GEF$ is $180^\circ$. So:
$$58^\circ + 16x + 90^\circ = 180^\circ$$

Step3: Simplify and solve for x

Combine constants first:
$$148^\circ + 16x = 180^\circ$$
Subtract $148^\circ$ from both sides:
$$16x = 180^\circ - 148^\circ = 32^\circ$$
Divide by 16:
$$x = \frac{32^\circ}{16} = 2^\circ$$

Answer:

$x = 2$