Question

name the marked angle in 2 different ways.

Explanation:

Step1: Identify the vertex and sides

The marked angle has vertex \( D \) and sides \( DQ \) and \( DP \) (or considering the other ray \( DE \), but the marked angle is between \( DQ \) and the middle ray, let's assume the marked angle is \( \angle QDP \) or using the single letter at vertex or with three points).

Step2: List the ways to name the angle

1. Using the vertex and two points on the sides: If the angle is between \( DQ \) and \( DP \) (assuming the middle ray is part of the angle? Wait, the diagram has \( D \) as vertex, rays \( DE \), \( D \) (middle ray), \( DQ \), \( DP \)? Wait, the marked angle is at \( D \), between \( DQ \) and the ray towards \( P \)? Wait, maybe the angle is \( \angle QDP \), \( \angle PDQ \), or using the vertex alone as \( \angle D \) (if it's the only angle at \( D \) for that, but usually with three points). Also, if there's a number, but the diagram doesn't show number. Wait, the problem says "name the marked angle in 2 different ways". So first way: using three points, with vertex in the middle: \( \angle QDP \). Second way: using the vertex letter: \( \angle D \) (if it's the only angle at \( D \) for that region). Or maybe the angle is between \( DQ \) and the other ray (let's say the middle ray is \( D \) (let's call the middle ray \( DM \), but in the diagram, the rays are \( DE \), \( D \) (middle), \( DQ \), \( DP \)? Wait, the diagram has \( D \) connected to \( E \) (ray \( DE \)), \( D \) connected to a middle ray, \( D \) connected to \( Q \) (ray \( DQ \)), \( D \) connected to \( P \) (ray \( DP \)). The marked angle is between \( DQ \) and the middle ray? Wait, maybe the marked angle is \( \angle QDP \) (if the middle ray is part of \( DP \)? No, \( DP \) is a ray. Wait, maybe the angle is at \( D \), between \( DQ \) and \( DP \), so first name: \( \angle QDP \), second name: \( \angle PDQ \). Or if the angle is between \( DQ \) and the ray from \( D \) to the middle (but maybe the diagram has the marked angle as \( \angle QDP \) and \( \angle D \) (if it's the only angle at \( D \) for that). Wait, standard angle naming:

• Using three points: \( \angle QDP \) (vertex \( D \), sides \( DQ \) and \( DP \))
• Using the vertex: \( \angle D \) (if there's only one angle at \( D \) for that, but usually when there are multiple angles, we use three points. But the problem says two different ways. So another way: if the angle is between \( DQ \) and the ray (let's say the middle ray is \( DM \), but maybe the diagram has the marked angle as \( \angle QDP \) and \( \angle PDQ \), or \( \angle D \) and \( \angle QDP \).

Wait, let's correct. The angle with vertex \( D \), and sides \( DQ \) and \( DP \) (assuming the marked angle is between \( DQ \) and \( DP \)). So:

First way: \( \angle QDP \) (three - point notation, vertex in the middle)

Second way: \( \angle PDQ \) (three - point notation, reversing the order of the points on the sides)

Or, if the angle is the only angle at \( D \) for that, we can also name it as \( \angle D \).

Answer:

Two ways to name the marked angle (assuming the angle is at \( D \) between \( DQ \) and \( DP \)) are \( \angle QDP \) and \( \angle PDQ \) (or \( \angle D \) and \( \angle QDP \) depending on the diagram's context).