Question

name each angle in four ways. 5) diagram with vertex g, ray gh (with point h), ray gf (with point f), angle labeled 5

Explanation:

Step1: Recall angle naming rules

An angle can be named by: 1) the vertex letter, 2) three letters with the vertex in the middle, 3) a number (if labeled), 4) a Greek letter or other symbol (if labeled, here we have number 5 and vertex \( G \), sides \( GH \) and \( GF \)).

Step2: Name using vertex

Using the vertex \( G \), the angle is \( \angle G \).

Step3: Name using three points (vertex middle)

The two sides are \( GH \) and \( GF \), so with \( G \) in the middle, it's \( \angle HGF \) or \( \angle FGH \).

Step4: Name using the number label

The angle is labeled with 5, so \( \angle 5 \).

Step5: Check another three - point name (consistent with sides)

Since the sides are \( GH \) (with \( H \) on one ray) and \( GF \) (with \( F \) on the other ray), the angle can also be named as \( \angle HGF \) (or \( \angle FGH \)) as in step 3, and combining with vertex and number, we have four ways: \( \angle G \), \( \angle HGF \), \( \angle FGH \), \( \angle 5 \).

Answer:

The four ways to name the angle are \( \angle G \), \( \angle HGF \), \( \angle FGH \), \( \angle 5 \)