Question

which name can be used for the 20° angle? ∠evt
how is ∠evt related to ∠nve?
both angles have a vertex at point?
both angles share the side?
options for the second blank: e, v, n, t
(image shows a coordinate system with point v at the origin, n (north), s (south), e (east), w (west), a 90° angle between n and e, and a 20° angle between e and t, with arrows from w to t and another arrow.)

Explanation:

Step1: Analyze the vertex of angles

An angle is named with the vertex in the middle. For \(\angle EVT\) and \(\angle NVE\), the vertex is the point where the two sides of the angle meet. Looking at the angle notation, the middle letter represents the vertex. So, the vertex of both \(\angle EVT\) and \(\angle NVE\) is point \(V\).

Step2: Analyze the shared side

A side of an angle is a ray. For \(\angle EVT\), the sides are \(VE\) and \(VT\). For \(\angle NVE\), the sides are \(VN\) and \(VE\). So, the shared side is \(VE\).

Answer:

Both angles have a vertex at point \(V\). Both angles share the side \(VE\).