Question

name the marked angle in 2 different ways.

Explanation:

Step1: Identify the vertex and rays

The angle has vertex \( N \), with one ray from \( N \) to \( M \) and another from \( N \) to \( P \), or considering the marked angle between \( M \), \( N \), \( P \) (wait, no, the marked angle is between \( M \), \( N \), and the other ray? Wait, the diagram: points \( M \), \( N \), \( P \) and \( O \). Wait, the marked angle is at \( N \), between \( M \) and \( P \)? Wait, no, the pink angle is between \( M \), \( N \), and \( P \)? Wait, no, the rays are \( NM \), \( NP \), and \( NO \)? Wait, no, the diagram shows: \( M \) on a left ray, \( P \) on a top-left ray, \( O \) on a right ray, all from \( N \). The marked angle (pink) is between \( NM \) and \( NP \)? Wait, no, maybe between \( M \), \( N \), \( P \)? Wait, no, let's check: the angle can be named by the vertex and two points (one on each ray), or by the vertex alone if it's unique.

Step2: Name the angle

First way: Using three points, with the vertex in the middle: \( \angle MNP \) (since the rays are \( NM \) and \( NP \), vertex \( N \)). Second way: Using the vertex alone (if there's only one angle at \( N \) for that, but here, maybe \( \angle PNM \) (same angle, reversed order) or \( \angle N \) (if it's the only angle at \( N \), but maybe the marked angle is between \( M \), \( N \), \( P \)). Wait, maybe the marked angle is \( \angle MNP \) and \( \angle PNM \), or \( \angle N \) (but usually, with three points, or vertex). Wait, let's see: the two rays forming the angle are \( NM \) and \( NP \), so the angle can be named \( \angle MNP \) (with vertex \( N \), between \( M \) and \( P \)) and \( \angle PNM \) (same angle, just reversed order of the points on the rays), or also \( \angle N \) if it's the only angle at \( N \), but more accurately, using three points.

Wait, maybe the diagram: the marked angle is at \( N \), between \( M \) (left ray) and \( P \) (top-left ray), so two names: \( \angle MNP \) and \( \angle PNM \), or \( \angle N \) (but usually, three-point notation is better). So first name: \( \angle MNP \), second name: \( \angle PNM \) (or \( \angle N \), but three-point is more precise).

Answer:

\( \angle MNP \) and \( \angle PNM \) (or \( \angle N \) if acceptable, but three-point is standard). So filling the boxes: first box: \( MNP \), second box: \( PNM \) (or \( N \) if allowed, but likely three-point).