Question

select the correct answers. if an angle is represented with three numbers: 1,2, and 3 and 3 is the origin of the two rays, which of the followings are be the angles names.
a ∠1,2,3
b ∠1,3,2
c ∠2
d ∠3
e ∠2,3,1
f ∠3,2,1

Explanation:

Step1: Recall the angle - naming rule

When naming an angle with three points, the vertex (the origin of the two rays) is in the middle.

Step2: Analyze each option

• Option A: In \(\angle1,2,3\), the vertex is not in the middle.
• Option B: In \(\angle1,3,2\), the vertex \(3\) is in the middle.
• Option C: \(\angle2\) is not a valid name as the vertex is \(3\).
• Option D: \(\angle3\) is a valid name (a single - letter name for the angle with vertex \(3\)).
• Option E: In \(\angle2,3,1\), the vertex \(3\) is in the middle.
• Option F: In \(\angle3,2,1\), the vertex is not in the middle.

Answer:

B. \(\angle1,3,2\), D. \(\angle3\), E. \(\angle2,3,1\)