Question

name the angle in three kinds of notation.
select all that apply.
□a. \\( \angle b c \\)
□b. \\( \angle c b \\)
□c. \\( \angle b \\)
□d. \\( \angle c \\)
□e. \\( \angle b c a \\) or \\( \angle a c b \\)

Explanation:

Step1: Recall angle - naming rules

An angle can be named in three ways: by the vertex (if there is only one angle at the vertex), by three points (with the vertex in the middle), or by a number or lowercase letter inside the angle.

Step2: Analyze each option

• Option A: $\angle BAC$: The vertex is \(A\), and the rays are \(AB\) and \(AC\). But in the given figure, the vertex of the angle is \(B\) (assuming the points are \(B\) as the vertex, and two rays from \(B\)). So this is incorrect.
• Option B: $\angle ABC$: The vertex is \(B\), and if the two rays are \(BA\) and \(BC\), this is a valid way to name the angle (three - point naming with the vertex in the middle).
• Option C: $\angle B$: If there is only one angle at vertex \(B\), then naming the angle by its vertex (\(\angle B\)) is a valid way.
• Option D: $\angle 1$: If the number \(1\) is inside the angle, then \(\angle 1\) is a valid name.
• Option E: $\angle BAC$ or $\angle ABC$: Since $\angle BAC$ is incorrect (vertex mismatch) and $\angle ABC$ is correct, this combined option is incorrect.

Answer:

B. \(\angle ABC\), C. \(\angle B\), D. \(\angle 1\)