Question

which of the following correctly names the angle shown? select all that apply. a) ∠b b) ∠c c) ∠1 d) ∠abc e) ∠bac f) ∠acb

Explanation:

To name an angle, we can use different notations:

• Using a number: like $\angle 1$ (option C) as the angle is labeled 1 at vertex B.
• Using three points with the vertex in the middle: $\angle ABC$ (option D) where B is the vertex, A and C are points on the sides.
• Using the vertex letter (when there's only one angle at the vertex): $\angle B$ (option A) since at point B, there's one angle formed by the line.
• $\angle ABC$ (D) is correct as it's a three - point notation with B as vertex. $\angle 1$ (C) is correct as it's the numbered angle. $\angle B$ (A) is correct as it's the vertex - named angle. $\angle ABC$: The middle letter is the vertex (B), and A and C are on the two sides of the angle. $\angle 1$: The angle is marked with 1. $\angle B$: Since there's only one angle at vertex B, we can name it by its vertex. Options B ($\angle C$) is incorrect as C is not the vertex. Option E ($\angle BAC$) has vertex A, which is wrong. Option F ($\angle ACB$) has vertex C, which is wrong.

Answer:

A. $\angle B$, C. $\angle 1$, D. $\angle ABC$