Question

a weathervane is pointing north. after the wind changes direction, the weathervane points east. the turn forms a right angle. how many degrees did the arrow turn? 90 you can name the turn ∠nve, because it connects points n, v, and e in order. what is another good name you could use for ∠nve? ∠n ∠v ∠evn ∠evs

Explanation:

For the angle - naming question:

To name an angle, the middle letter should be the vertex. For \(\angle NVE\), the vertex is \(V\). Let's analyze each option:

• \(\angle N\): The vertex here would be \(N\), but the angle in question has vertex \(V\), so this is incorrect.
• \(\angle V\): When the vertex is a single letter (and there is only one angle at that vertex, which is the case here as the angle at \(V\) between \(N\) and \(E\) is a right angle and there's no ambiguity), we can name the angle by its vertex. So \(\angle V\) is a valid name for \(\angle NVE\).
• \(\angle EVN\): When we name an angle, the order of the points can be reversed as long as the vertex is in the middle. For \(\angle NVE\), reversing the non - vertex points ( \(N\) and \(E\)) gives \(\angle EVN\), with \(V\) still as the vertex. This is also a valid name.
• \(\angle EVS\): The angle \(\angle EVS\) has sides \(EV\) and \(VS\), but our angle has sides \(NV\) and \(EV\), so this is incorrect.

Answer:

\(\angle V\), \(\angle EVN\)