Question

Which of these are valid names for the angle shown? Choose all that apply. (2 points) Responses ∠B ∠B ∠C ∠C ∠ABC ∠ABC ∠BCA

Answer 1

Pick two answers

Answer 2

To determine the valid names for an angle, we consider a few rules:

1. An angle can be named using one of its vertex points, provided it is the only angle at that vertex. For instance, if the angle's vertex is at point B, it can be named ∠B.
2. An angle can also be named using three points, where the middle point is the vertex of the angle. For example, if the angle is formed by points A, B, and C with B as the vertex, it can be named ∠ABC or ∠BCA.

Based on this information, the valid names for the angle shown would be as follows:

- ∠B (if it's the only angle at B, valid)
- ∠C (if it's the only angle at C, valid)
- ∠ABC (if A and C are points on the rays forming the angle at B)
- ∠BCA (if A and C are points on the rays forming the angle at B)

Without the specific diagram or context, we typically assume that:

- If the angle is at vertex B, then ∠B is valid.
- If the angle includes points A and C at vertex B, then both ∠ABC and ∠BCA are valid.
- ∠C would only be valid if it is the only angle at vertex C.

Thus, if these criteria apply, the valid names would likely be ∠B, ∠ABC, ∠BCA, and possibly ∠C, depending on the vertices involved.

Answer 3

Based on the information about naming angles, if I have to select only two valid names for the angle shown, I would choose:

1. ∠ABC (assuming points A and C are defining the angle at point B)
2. ∠B (if the angle is specifically centered at that vertex)

These choices cover both the naming by vertex and by the three-point method commonly used.