Question

name the marked angle in 2 different ways.
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Explanation:

Step1: Identify the vertex and rays

The marked angle has vertex \( E \), and the two rays forming it are \( ED \) and \( EG \), or we can also consider the middle ray \( EG \) with \( EF \), but wait, no—the marked angle is between \( ED \) and \( EG \)? Wait, no, looking at the diagram, the pink angle is between \( ED \) and \( EG \)? Wait, no, the points are \( D \), \( E \), \( G \), \( F \). Wait, the vertex is \( E \), and the two sides are \( ED \) and \( EG \), or maybe \( DE \) and \( GE \), but angle naming: one way is using the vertex and two points on the rays, so \( \angle DEG \), and another way is using the vertex alone if there's only one angle at \( E \), but here maybe \( \angle GED \) or \( \angle E \) (but usually, if there are multiple angles at \( E \), we use three points). Wait, the marked angle is between \( ED \) and \( EG \), so first way: \( \angle DEG \), second way: \( \angle GED \), or also \( \angle E \) but maybe the diagram has only that angle marked, so two ways: \( \angle DEG \) and \( \angle GED \), or \( \angle E \) but probably three - point notation. Wait, let's check: the angle is formed by \( ED \) and \( EG \), so vertex \( E \), with points \( D \) and \( G \) on the rays. So first name: \( \angle DEG \) (order: \( D \) - \( E \) - \( G \)), second name: \( \angle GED \) (order: \( G \) - \( E \) - \( D \)). Alternatively, maybe the angle is between \( ED \) and \( EG \), so two ways: \( \angle DEG \) and \( \angle E \) (if only one angle at \( E \)), but more accurately, with three points. So:

Step2: Write the two names

First, using three points with \( D \), \( E \), \( G \): \( \angle DEG \). Second, using the vertex and the two rays, or reversing the order: \( \angle GED \). Or maybe the angle is between \( ED \) and \( EG \), so another way: \( \angle E \) (but usually, three - point is better). Wait, let's confirm: angle at \( E \), between \( ED \) and \( EG \), so \( \angle DEG \) (with \( D \) on one ray, \( E \) vertex, \( G \) on the other ray) and \( \angle GED \) (reversing the order of the points on the rays).

Answer:

\( \angle DEG \) and \( \angle GED \) (or \( \angle E \) if only one angle, but three - point is more precise here)

Wait, maybe I made a mistake. Wait, the diagram: points \( D \), \( E \), \( G \), \( F \). The pink angle is between \( ED \) and \( EG \), so two ways: \( \angle DEG \) and \( \angle GED \), or also, if we consider the middle ray \( EG \) and \( EF \), but no, the marked angle is between \( ED \) and \( EG \). So the two names are \( \angle DEG \) and \( \angle GED \), or \( \angle E \) (but three - point is standard when there are multiple angles at the vertex). So filling in the boxes: first box \( DEG \), second box \( GED \) (or \( E \), but likely three - point).