Question

which are other possible names for ∠3? choose all answers that are correct.
□ <e
□ <fer
□ <pre
□ <aep
□ <fep
□ <def

Explanation:

Step1: Recall angle - naming rules

An angle can be named by its vertex letter (if there is only one angle at that vertex), by three points where the middle point is the vertex, or by a number. For ∠3, the vertex is E.

Step2: Check each option

• ∠E: An angle can be named by its vertex when there is only one angle at that vertex. Here, at vertex E, ∠3 is the only angle, so ∠E is a valid name.
• ∠FER: The vertex of the angle is E, and the points F and R are on the rays forming the angle. So ∠FER is a valid name.
• ∠PRE: The vertex here is P, and it does not represent ∠3, so it is not a valid name.
• ∠AEP: The vertex is E, but the points A and P do not form the same angle as ∠3, so it is not a valid name.
• ∠FEP: The vertex is E, and the points F and P are on the rays forming the angle, so ∠FEP is a valid name.
• ∠DEF: The vertex is E, but the points D and F do not form the same angle as ∠3, so it is not a valid name.

Answer:

∠E, ∠FER, ∠FEP