Question

which is a correct name for the angle shown?

Explanation:

Step1: Recall angle - naming rules

An angle can be named in three ways: by a single letter (if there is only one angle at that vertex), by three letters with the vertex letter in the middle.

Step2: Analyze each option

• For \(\angle A\): There are multiple angles at vertex \(A\) (the angle formed by \(BA\) and its extension), so \(\angle A\) is not a unique name for the angle in question.
• For \(\angle CBA\): The vertex is \(B\). But the angle in question has vertex \(B\) and the rays \(BA\) and \(BC\). However, \(\angle CBA\) is the angle at \(B\) with sides \(BC\) and \(BA\) in the opposite orientation of what we might expect if we follow the standard naming (usually we name angles based on the sides we are interested in. Here, if we consider the angle formed by the two rays starting from \(B\) (one going to \(A\) and one going to \(C\)), but the notation \(\angle CBA\) is not the most standard for the angle shown.
• For \(\angle C\): There are multiple angles at vertex \(C\) (the straight - line angle and other possible angles if we consider the figure's context), so \(\angle C\) is not a unique name.
• For \(\angle ACB\): The vertex is \(C\). The angle is formed by the rays \(CA\) and \(CB\). According to the three - letter naming rule (vertex in the middle), \(\angle ACB\) is a correct name for the angle formed at vertex \(C\) with sides \(CA\) and \(CB\).

Answer:

\(\angle ACB\)