Question

naming angles
name the vertex and sides of each angle.
1)
3)
name each angle in four ways.
5)
7)
draw and label an angle to fit each description.

1. an obtuse angle, ∠y
2. a right angle, ∠3

2)
4)
6)
8)

1. an acute angle, ∠jih
2. a straight angle, ∠cde

Explanation:

Step1: Define vertex and sides of an angle

The vertex is the common endpoint of the rays that form the angle, and the sides are the two rays.
For the angle with points \(N\), \(M\), \(L\) (assuming \(M\) is the vertex), vertex is \(M\), sides are rays \(\overrightarrow{MN}\) and \(\overrightarrow{ML}\).

Step2: Name an angle in four - ways

For an angle with vertex \(C\) and points \(D\) and \(E\) around it:

1. By the vertex only: \(\angle C\)
2. By three points with vertex in the middle: \(\angle DCE\)
3. By three points with vertex in the middle in reverse order: \(\angle ECD\)
4. By a number (if labeled): If there is a number \(3\) at the angle, it can be called \(\angle 3\)

Step3: Draw different types of angles

• Obtuse angle \(\angle Y\): Draw an angle that measures more than \(90^{\circ}\) but less than \(180^{\circ}\), label the vertex as \(Y\) and the rays as appropriate.
• Acute angle \(\angle JIH\): Draw an angle that measures less than \(90^{\circ}\), label the vertex \(I\) and the rays \(\overrightarrow{IJ}\) and \(\overrightarrow{IH}\).
• Right angle \(\angle 3\): Draw an angle that measures \(90^{\circ}\), label the vertex and the rays and mark the right - angle symbol, and label the angle as \(\angle 3\).
• Straight angle \(\angle CDE\): Draw an angle that measures \(180^{\circ}\), label the vertex \(D\) and the rays \(\overrightarrow{DC}\) and \(\overrightarrow{DE}\).

Answer:

1. For the first part (naming vertex and sides), answers vary depending on the specific angle. For example, if considering the angle with points \(N\), \(M\), \(L\) (where \(M\) is the vertex), vertex: \(M\), sides: \(\overrightarrow{MN}\), \(\overrightarrow{ML}\).
2. For naming an angle in four ways (e.g., for an angle with vertex \(C\) and points \(D\), \(E\)): \(\angle C\), \(\angle DCE\), \(\angle ECD\), (if numbered) \(\angle\) (number).
3. For drawing angles:

• Obtuse angle \(\angle Y\): Draw an angle greater than \(90^{\circ}\) and less than \(180^{\circ}\) with vertex \(Y\).
• Acute angle \(\angle JIH\): Draw an angle less than \(90^{\circ}\) with vertex \(I\).
• Right angle \(\angle 3\): Draw a \(90^{\circ}\) angle and label it \(\angle 3\).
• Straight angle \(\angle CDE\): Draw a \(180^{\circ}\) angle with vertex \(D\).