Question

name the marked angle in 2 different ways.
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Explanation:

Step1: Identify the vertex and sides

The marked angle has vertex \( Q \), and its sides are \( QT \) and \( QR \) (or \( QS \) and \( QT \)? Wait, no, the marked angle is at \( Q \), between \( QT \) and \( QR \)? Wait, looking at the diagram, the marked angle is at \( Q \), with one side \( QT \) and another \( QR \)? Wait, no, the points are \( Q \), \( T \), \( R \), \( S \). So the marked angle is \( \angle TQR \) or \( \angle Q \) (using the vertex letter). Wait, angle naming: either using three letters with the vertex in the middle, or using the vertex letter alone if there's only one angle at that vertex. Here, at \( Q \), the marked angle is between \( QT \) and \( QR \), so one way is \( \angle TQR \), another way is \( \angle Q \) (since there's only one marked angle at \( Q \)). Wait, but maybe the sides are \( QT \) and \( QS \)? Wait, no, the diagram: \( Q \) connected to \( T \), \( R \), \( S \). The marked angle is at \( Q \), between \( QT \) and \( QR \)? Or between \( QT \) and \( QS \)? Wait, the pink angle is at \( Q \), with one side \( QT \) and another \( QR \) or \( QS \)? Wait, let's see: the triangle \( QTS \) and \( QTR \)? Wait, maybe the marked angle is \( \angle TQR \) (three letters: \( T \)-\( Q \)-\( R \)) and \( \angle Q \) (vertex letter). Alternatively, maybe \( \angle SQT \)? No, the pink angle is between \( QT \) and \( QR \), I think. Wait, maybe the correct names are \( \angle TQR \) and \( \angle Q \). Or \( \angle RQT \) (same as \( \angle TQR \)) and \( \angle Q \).

Step2: Confirm the angle names

First way: using three points, with \( Q \) as the vertex, so \( \angle TQR \) (or \( \angle RQT \)). Second way: using the vertex letter alone, \( \angle Q \), since there's only one marked angle at \( Q \).

Answer:

\( \angle TQR \) (or \( \angle RQT \)) and \( \angle Q \)

Wait, but maybe the sides are \( QT \) and \( QS \)? Wait, no, the pink angle is between \( QT \) and \( QR \), I think. Alternatively, maybe \( \angle SQT \) and \( \angle Q \), but no, the diagram shows \( T \) on \( QS \)? Wait, \( S \) is connected to \( T \), so \( QT \) is a segment from \( Q \) to \( T \) on \( QS \). So the marked angle is at \( Q \), between \( QT \) and \( QR \), so \( \angle TQR \) (or \( \angle RQT \)) and \( \angle Q \).

So the two ways are \( \angle TQR \) (or \( \angle RQT \)) and \( \angle Q \).