Question

which of the following is not a name of the angle? a c t <act <tac <a <cat

Explanation:

Step1: Recall angle - naming rules

An angle can be named using the vertex - point in the middle when three points are used (e.g., $\angle BAC$ where $A$ is the vertex), or just by the vertex - point when there is only one angle at that vertex (e.g., $\angle A$).
For the given angle with vertex $A$ and rays $AC$ and $AT$, the valid names are $\angle TAC$, $\angle CAT$ and $\angle A$ since $A$ is the vertex.

Step2: Analyze each option

• $\angle ACT$ has vertex $C$, but the angle in the figure has vertex $A$. So $\angle ACT$ is not a name for the given angle.
• $\angle TAC$ is a valid name as the vertex is $A$ and the rays are $AT$ and $AC$.
• $\angle A$ is a valid name since $A$ is the only vertex of the angle.
• $\angle CAT$ is a valid name with vertex $A$ and rays $CA$ and $CT$.

Answer:

$\angle ACT$