Question

name the marked angle in 2 different ways.

Explanation:

Step1: Identify the vertex and sides

The marked angle has vertex \( P \), and its sides are \( PN \) and \( PQ \). So one way to name it is using the vertex and the two points on the sides: \( \angle NPQ \).

Step2: Use the vertex alone (if unique)

Since at vertex \( P \), the marked angle is between \( PN \) and \( PQ \), and if there's no confusion (the diagram shows this specific angle at \( P \) between \( PN \) and \( PQ \)), we can also name it as \( \angle P \) (though more precisely, when using the vertex alone, it's assumed the angle is the one formed by the relevant sides; alternatively, using the three - letter notation with vertex in the middle is more precise, but another valid way is \( \angle QPN \) as well, but we'll use \( \angle NPQ \) and \( \angle P \) (or \( \angle QPN \)). Wait, more accurately, the two common ways are:

1. Using three points with the vertex in the middle: \( \angle NPQ \) (where \( N \) and \( Q \) are on the two sides, and \( P \) is the vertex).
2. Using the vertex letter: \( \angle P \) (since at point \( P \), the marked angle is the one between \( PN \) and \( PQ \), and if there's only one angle at \( P \) being considered here, this is valid. Alternatively, \( \angle QPN \) is also a three - letter notation with the vertex in the middle, just reversing the order of the points on the sides.

Answer:

Two ways to name the marked angle are \( \angle NPQ \) and \( \angle P \) (or \( \angle QPN \) and \( \angle NPQ \))