Question

name the marked angle in 2 different ways.

Explanation:

Step1: Identify the vertex and rays

The marked angle has vertex \( B \), and the two rays forming it are \( BE \) (or \( BC \), considering the position) and \( BB \)? Wait, no. Wait, the angle is at \( B \), between \( BE \) (or \( BC \)) and \( BB \)? Wait, no, looking at the diagram, the marked angle at \( B \) is between \( BE \) (or \( BC \)) and \( BB \)? Wait, no, the points are \( B \), \( E \), \( C \), \( D \). Wait, the marked angle is at \( B \), with one side along \( BC \) (or \( BE \)) and the other along \( BB \)? Wait, no, the vertex is \( B \), and the two sides are \( BE \) (or \( BC \)) and \( BB \)? Wait, no, the angle is \( \angle EBC \)? Wait, no, the marked angle is at \( B \), between \( BE \) (or \( BC \)) and \( BB \)? Wait, no, the correct way: angle can be named by the vertex, or by three points (with vertex in the middle). So the vertex is \( B \), so one name is \( \angle B \). Another name is using three points: the two sides are \( BE \) (or \( BC \)) and \( BB \)? Wait, no, looking at the diagram, the marked angle is at \( B \), between \( BE \) (or \( BC \)) and \( BB \)? Wait, no, the points are \( B \), \( E \), \( C \), \( D \). So the angle is formed by rays \( BB \)? No, wait, the vertex is \( B \), and the two sides are \( BE \) (or \( BC \)) and \( BB \)? No, that's not right. Wait, the angle is \( \angle EBC \)? Wait, no, the marked angle is at \( B \), so let's see: the angle is between \( BE \) (or \( BC \)) and \( BB \)? No, the correct names: first, by the vertex: \( \angle B \). Second, by three points: the two sides are \( BC \) (or \( BE \)) and \( BB \)? Wait, no, the angle is \( \angle EBC \) or \( \angle CBE \), but also, since it's at \( B \), we can name it \( \angle B \) (if there's only one angle at \( B \), but here there are multiple, but the marked one is between \( BE \) (or \( BC \)) and \( BB \)? Wait, no, the diagram shows the marked angle at \( B \), with one side towards \( E \) (or \( C \)) and the other towards... Wait, maybe the angle is \( \angle EBC \) and \( \angle B \) (but actually, when there are multiple angles at a vertex, we use three points. Wait, the marked angle is between \( BE \) and \( BC \)? No, the arrow is pointing to the angle at \( B \), between \( BE \) (or \( BC \)) and \( BB \)? Wait, no, the vertex is \( B \), so the angle can be named as \( \angle B \) (if it's the only angle, but here maybe it's \( \angle EBC \) and \( \angle CBE \), but also, another way: \( \angle B \) (but actually, the standard ways are: 1. Using the vertex: \( \angle B \) (if unique), 2. Using three points: \( \angle EBC \) (with \( B \) as vertex, \( E \) and \( C \) as the other two points). Wait, maybe the angle is \( \angle EBC \) and \( \angle B \). Wait, let's correct: the angle at \( B \), formed by \( BE \) and \( BC \) (or \( BE \) and \( BB \)? No, the points are \( B \), \( E \), \( C \), \( D \). So the marked angle is \( \angle EBC \) (or \( \angle CBE \)) and \( \angle B \) (if we consider the vertex). Wait, actually, the two ways are: 1. \( \angle B \) (using the vertex), 2. \( \angle EBC \) (using three points, with \( B \) in the middle).

Step2: Confirm the names

So the first way is using the vertex: \( \angle B \). The second way is using three points: \( \angle EBC \) (or \( \angle CBE \), but usually, the middle letter is the vertex). So the two names are \( \angle B \) and \( \angle EBC \) (or \( \angle CBE \)).

Answer:

Two ways to name the marked angle are \( \angle B \) and \( \angle EBC \) (or \( \angle CBE \)).