Use the image to answer the question.

Question

An illustration shows two leftward rays emerging from a point and the internal angle is marked e. A vertical line emerging from the top ray forms an angle with the ray labeled f.

Determine if the two indicated angles are adjacent.

(1 point)
Responses

Yes, they share a common vertex.
Yes, they share a common vertex.

Yes, they share a common ray.
Yes, they share a common ray.

No, they do not share a common vertex.
No, they do not share a common vertex.

No, they do not share a common ray.

Answer 1

To determine if the angles \( e \) and \( f \) are adjacent, we need to check if they share a common vertex and/or a common ray.

• Common Vertex: Both angles share the same vertex where the rays originate. Since both angles emerge from a point, they share a common vertex.

• Common Ray: For two angles to be adjacent, they must also share a common ray. The angle \( e \) is formed between the two leftward rays, while the angle \( f \) is formed with one of those rays (the top ray). If angle \( f \) shares one of the rays with angle \( e \), then they also share a common ray.

Based on this information, since angles \( e \) and \( f \) share a common vertex (the point where the rays originate) and share a common ray (the top ray), the correct response is that they are indeed adjacent angles.

Therefore, the answer is:

Yes, they share a common vertex.