Asked by kyle smith
Use the image to answer the 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.
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.
Answers
Answered by
GPT-4o mini
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.**
- **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.**
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