Question

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

Explanation:

When naming an angle with three - letter notation, the vertex (the origin of the two rays) is the middle letter. Here, the vertex is \(a\). Also, an angle can be named by its vertex (when there is no confusion).

• Option A: \(\angle a,b,c\) is an incorrect three - letter notation as the vertex \(a\) is not in the middle.
• Option B: \(\angle a\) is a valid name (when there is only one angle at vertex \(a\)).
• Option C: \(\angle b\) is incorrect as \(b\) is not the vertex.
• Option D: \(\angle c\) is incorrect as \(c\) is not the vertex.
• Option E: \(\angle c,a,b\) has the vertex \(a\) in the middle, so it is a valid three - letter notation.
• Option F: \(\angle b,c,a\) has the vertex \(c\) (incorrect as the vertex is \(a\)).

Answer:

B. \(\angle a\), E. \(\angle c,a,b\)