Question

name the vertex and sides of each angle. 1) 2) 3) 4) name each angle in four ways. 5) 6) 7) 8)

Explanation:

Step1: Recall angle - vertex and side definitions

The vertex of an angle is the common endpoint of the two rays that form the angle, and the sides are the two rays.

Step2: Analyze angle 1

The vertex of the angle in 1) is \(M\). The sides are rays \(\overrightarrow{MN}\) and \(\overrightarrow{ML}\).

Step3: Analyze angle 2

The vertex of the angle in 2) is \(D\). The sides are rays \(\overrightarrow{DE}\) and \(\overrightarrow{DC}\).

Step4: Analyze angle 3

The vertex of the angle in 3) is \(R\). The sides are rays \(\overrightarrow{RS}\) and \(\overrightarrow{RQ}\).

Step5: Analyze angle 4

The vertex of the angle in 4) is \(T\). The sides are rays \(\overrightarrow{TS}\) and \(\overrightarrow{TU}\).

Step6: Recall angle - naming conventions

An angle can be named by the vertex (if there is only one angle at that vertex), by three points (with the vertex in the middle), by a number, or by a Greek letter.

Step7: Name angle 5

The four ways to name the angle in 5) are \(\angle 3\), \(\angle EDC\), \(\angle CDE\), \(\angle D\).

Step8: Name angle 6

The four ways to name the angle in 6) are \(\angle 4\), \(\angle EFG\), \(\angle GFE\), \(\angle F\).

Step9: Name angle 7

The four ways to name the angle in 7) are \(\angle 1\), \(\angle EFG\), \(\angle GFE\), \(\angle F\).

Step10: Name angle 8

The four ways to name the angle in 8) are \(\angle 3\), \(\angle JIH\), \(\angle HIJ\), \(\angle I\).

Answer:

1. Vertex: \(M\), Sides: \(\overrightarrow{MN}\), \(\overrightarrow{ML}\)
2. Vertex: \(D\), Sides: \(\overrightarrow{DE}\), \(\overrightarrow{DC}\)
3. Vertex: \(R\), Sides: \(\overrightarrow{RS}\), \(\overrightarrow{RQ}\)
4. Vertex: \(T\), Sides: \(\overrightarrow{TS}\), \(\overrightarrow{TU}\)
5. \(\angle 3\), \(\angle EDC\), \(\angle CDE\), \(\angle D\)
6. \(\angle 4\), \(\angle EFG\), \(\angle GFE\), \(\angle F\)
7. \(\angle 1\), \(\angle EFG\), \(\angle GFE\), \(\angle F\)
8. \(\angle 3\), \(\angle JIH\), \(\angle HIJ\), \(\angle I\)