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

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

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 ray.
No, they do not share a common ray.
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page 12 of 12

Answer 1

To determine if the two indicated angles \( e \) and \( f \) are adjacent, we need to consider the definitions of adjacent angles.

Adjacent angles are defined as two angles that:

1. Share a common vertex (the point where the two rays meet).
2. Share a common ray (one ray of each angle is the same).
3. Do not overlap.

Based on your description, since \( e \) and \( f \) both emerge from the same point (the vertex) and do not overlap but share a common ray (the ray from the vertex that forms part of angle \( e \) and angle \( f \)), it implies that they are indeed adjacent angles.

So the correct response is:

Yes, they share a common vertex.