Question

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

Explanation:

Step1: Recall the angle - naming rule

When an angle is named with three letters, the middle letter is the vertex (the origin of the two rays). Also, an angle can be named by its vertex alone.

Step2: Analyze each option

• Option A: \(\angle xyz\): The vertex should be in the middle. Here, \(y\) is the middle letter, not \(x\). So this is incorrect.
• Option B: \(\angle zxy\): The middle letter \(x\) is the vertex. This is a valid name.
• Option C: \(\angle zyx\): The middle letter \(y\) is not the vertex (\(x\) is the vertex). So this is incorrect.
• Option D: \(\angle x\): Since \(x\) is the vertex, this is a valid name.
• Option E: \(\angle z\): \(z\) is not the vertex. So this is incorrect.
• Option F: \(\angle yxz\): The middle letter \(x\) is the vertex. This is a valid name.

Answer:

B. \(\angle zxy\), D. \(\angle x\), F. \(\angle yxz\)