The county name refers to several municipalities together.
The county charter lists its 19 towns and municipalities individually. They include places on both sides of the Rhine. The administrative seat, Siegburg, is itself one of those towns; it must not be equated with the whole county territory.
Bonn is an important reference point for locating the county. However, the city is not one of its 19 member municipalities. The phrase around Bonn therefore describes proximity, rather than Bonn belonging to the county.
The other three answers
The other county names belong to different federal states.
Ammerland
Ammerland is in Niedersachsen. This county in north-western Germany does not belong to North Rhine-Westphalia.
Nordfriesland
Nordfriesland is in Schleswig-Holstein on the North Sea. Nord in its name does not make it a county of North Rhine-Westphalia.
Vogtlandkreis
Vogtlandkreis is in Saxony. It is geographically and administratively distinct from Rhein-Sieg-Kreis.
County, electoral district and landscape are different concepts.
A Landkreis or Kreis is a local territorial authority. An electoral district serves a particular election and can have different boundaries. The question asks for the official territorial unit Rhein-Sieg-Kreis.
The names Rhine and Sieg help with learning, but do not replace official classification. Other counties also lie along rivers. The charter and actual member municipalities provide reliable reference points here.
Section 1 · Name, seat and territory · Rhein-Sieg-Kreis · county charter ↗Rhein-Sieg-Kreis → North Rhine-Westphalia; seat → Siegburg.
Alfter and Troisdorf are two examples within the county.
Three words for this question
- der Kreiscounty
- A local territorial unit containing several towns and municipalities.
- kreisangehörigbelonging to a county
- Describes a municipality that forms part of a county.
- die Hauptsatzungprincipal charter
- A basic local charter defining, among other matters, the county’s name, seat and territory.