Question

after another wind change, the weathervane has turned an additional 20° and stopped at point t. which name can be used for the 20° angle? ∠ett how is ∠ett related to ∠nve? both angles have a vertex at point? both angles share the side?

Explanation:

Step1: Name of the \(20^{\circ}\) angle

An angle can be named using three points where the middle point is the vertex. For the \(20^{\circ}\) angle, the vertex is \(V\), and the two rays are \(VE\) and \(VT\). So the angle can be named \(\angle EVT\).

Step2: Relationship between \(\angle EVT\) and \(\angle NVE\)

Both \(\angle EVT\) and \(\angle NVE\) are adjacent angles. Adjacent angles have a common vertex and a common side.

Step3: Vertex of the angles

The vertex of an angle is the common point of the two rays forming the angle. For \(\angle EVT\) and \(\angle NVE\), the vertex is point \(V\).

Step4: Common side of the angles

Looking at the diagram, \(\angle EVT\) has sides \(VE\) and \(VT\), and \(\angle NVE\) has sides \(NV\) and \(VE\). The common side is \(VE\).

Answer:

• The \(20^{\circ}\) angle can be named \(\angle EVT\).
• \(\angle EVT\) and \(\angle NVE\) are adjacent angles.
• Both angles have a vertex at point \(V\).
• Both angles share the side \(VE\).