Question

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

Explanation:

Step1: Identify right angle

Since $EF$ is a diameter, $\angle EGF = 90^\circ$ (angle inscribed in a semicircle is a right angle).

Step2: Calculate $\angle E$

Use triangle angle sum: $\angle E + \angle F + \angle G = 180^\circ$.
$\angle E = 180^\circ - 90^\circ - 32^\circ$

Answer:

$58^\circ$