1. The problem asks to name points, line segments, rays, and angles based on the given figure with lines a and b intersecting at point X. 2. Three points on line a are: P, X, Q. 3. Three points on line b are: S, X, T. 4. Another name for line a is \( \overleftrightarrow{PQ} \) or \( \overleftrightarrow{QP} \). 5. Another name for line b is \( \overleftrightarrow{ST} \) or \( \overleftrightarrow{TS} \). 6. Three line segments on line a are: \( \overline{PX} \), \( \overline{XQ} \), and \( \overline{PQ} \). 7. Three line segments on line b are: \( \overline{SX} \), \( \overline{XT} \), and \( \overline{ST} \). 8. Four rays on line a are: \( \overrightarrow{PX} \), \( \overrightarrow{XQ} \), \( \overrightarrow{XP} \), and \( \overrightarrow{QX} \). 9. Four rays on line b are: \( \overrightarrow{SX} \), \( \overrightarrow{XT} \), \( \overrightarrow{XS} \), and \( \overrightarrow{TX} \). 10. Three different names for the plane determined by lines a and b can be: Plane \( PXS \), Plane \( QXT \), or Plane \( PQST \) (using any three non-collinear points on the plane). 11. Four angles formed by the intersecting lines a and b at point X are: \( \angle PX S \), \( \angle S X Q \), \( \angle Q X T \), and \( \angle T X P \). These names follow standard geometric notation where points are capital letters, lines are named by two points with a double arrow, segments by two points with a bar, rays by two points with an arrow, and angles by three points with the vertex in the middle.