Question

1. which of the following is not a proper way to name the angle shown below?

a. ∠acb
b. ∠abc
c. ∠cba
d. ∠b
e. ∠3

Explanation:

Step1: Recall angle - naming rules

An angle can be named using the vertex letter alone (if there is only one angle at that vertex), by three - letter notation with the vertex letter in the middle, or by a number assigned to the angle.

Step2: Analyze each option

• Option a: $\angle ACB$ follows the three - letter naming convention with vertex $C$ in the middle.
• Option b: $\angle ABC$ has the wrong vertex in the middle. The vertex of the given angle is $B$, not $A$.
• Option c: $\angle CBA$ follows the three - letter naming convention with vertex $B$ in the middle.
• Option d: $\angle B$ is a valid name since $B$ is the only angle at that vertex.
• Option e: $\angle3$ is a valid name if the angle is labeled with the number $3$.

Answer:

b. $\angle ABC$