Question

choose the correct answer. which means the same as ∠efg? ∠gfe ∠f ∠gfh

Explanation:

Step1: Recall angle - naming rules

An angle can be named in three ways: by three capital letters (with the vertex letter in the middle), by a single capital letter (the vertex letter, when there is no ambiguity), or by a number or symbol. For \(\angle EFG\), the vertex is \(F\).

Step2: Analyze each option

• For \(\angle GFE\): The vertex is \(F\), and using the three - letter naming rule (\(G - F - E\) with \(F\) as the vertex), it represents the same angle as \(\angle EFG\) (since the order of the non - vertex letters can be reversed when naming an angle with three letters).
• For \(\angle F\): If there are multiple angles at vertex \(F\) (in this case, \(\angle EFG\) and \(\angle GFH\) are at vertex \(F\)), using a single - letter name (\(\angle F\)) is ambiguous.
• For \(\angle GFH\): The vertex is \(F\), but the angle formed by points \(G\), \(F\), and \(H\) is a different angle from \(\angle EFG\) (as the non - vertex points \(E\) and \(H\) are on opposite sides of the ray \(FG\)).

Answer:

\(\angle GFE\)