Question

kuta software - infinite geometry
naming angles
name the vertex and sides of each angle.
1)
2)
3)
4)
name each angle in four ways.
5)
6)
7)
8)
draw and label an angle to fit each description.

1. an obtuse angle, ∠y
2. an acute angle, ∠jih
3. a right angle, ∠3
4. a straight angle, ∠cde

Explanation:

Step1: Recall angle - naming rules

The vertex of an angle is the common endpoint of the two rays that form the angle. The sides of an angle are the two rays. To name an angle in four ways: 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 letter.

Step2: Analyze problem 1

For the angle with points \(N\), \(M\), and \(L\):
- Vertex: \(M\)
- Sides: Rays \(\overrightarrow{MN}\) and \(\overrightarrow{ML}\)
- Four - way naming: \(\angle M\), \(\angle NML\), \(\angle LMN\), if it is labeled with a number or letter, we can also use that label.

Step3: Analyze problem 2

For the angle with points \(C\), \(D\), and \(E\):
- Vertex: \(D\)
- Sides: Rays \(\overrightarrow{DC}\) and \(\overrightarrow{DE}\)
- Four - way naming: \(\angle D\), \(\angle CDE\), \(\angle EDC\), if it is labeled with a number or letter, we can also use that label.

Step4: Analyze problem 3

For the angle with points \(S\), \(R\), and \(Q\):
- Vertex: \(R\)
- Sides: Rays \(\overrightarrow{RS}\) and \(\overrightarrow{RQ}\)
- Four - way naming: \(\angle R\), \(\angle SRQ\), \(\angle QRS\), if it is labeled with a number or letter, we can also use that label.

Step5: Analyze problem 4

For the angle with points \(S\), \(T\), and \(U\):
- Vertex: \(T\)
- Sides: Rays \(\overrightarrow{TS}\) and \(\overrightarrow{TU}\)
- Four - way naming: \(\angle T\), \(\angle STU\), \(\angle UTS\), if it is labeled with a number or letter, we can also use that label.

Step6: Analyze problem 5

For the angle with points \(E\), \(D\), and \(C\):
- Vertex: \(D\)
- Sides: Rays \(\overrightarrow{DE}\) and \(\overrightarrow{DC}\)
- Four - way naming: \(\angle D\), \(\angle EDC\), \(\angle CDE\), \(\angle3\) (since it is labeled as \(\angle3\))

Step7: Analyze problem 6

For the angle with points \(G\), \(F\), and \(E\):
- Vertex: \(F\)
- Sides: Rays \(\overrightarrow{FG}\) and \(\overrightarrow{FE}\)
- Four - way naming: \(\angle F\), \(\angle GFE\), \(\angle EFG\), \(\angle4\) (since it is labeled as \(\angle4\))

Step8: Analyze problem 7

For the angle with points \(E\), \(F\), and \(G\):
- Vertex: \(F\)
- Sides: Rays \(\overrightarrow{FE}\) and \(\overrightarrow{FG}\)
- Four - way naming: \(\angle F\), \(\angle EFG\), \(\angle GFE\), \(\angle1\) (since it is labeled as \(\angle1\))

Step9: Analyze problem 8

For the angle with points \(J\), \(I\), and \(H\):
- Vertex: \(I\)
- Sides: Rays \(\overrightarrow{IJ}\) and \(\overrightarrow{IH}\)
- Four - way naming: \(\angle I\), \(\angle JIH\), \(\angle HIJ\), \(\angle3\) (since it is labeled as \(\angle3\))

Step10: Analyze problem 9

To draw an obtuse angle \(\angle Y\):
Draw a ray \(\overrightarrow{YA}\). Then, using a protractor, draw another ray \(\overrightarrow{YB}\) such that the measure of \(\angle AYB\) is between \(90^{\circ}\) and \(180^{\circ}\). Label the vertex as \(Y\) and the rays as \(\overrightarrow{YA}\) and \(\overrightarrow{YB}\).

Step11: Analyze problem 10

To draw an acute angle \(\angle JIH\):
Draw a ray \(\overrightarrow{IJ}\). Then, using a protractor, draw another ray \(\overrightarrow{IH}\) such that the measure of \(\angle JIH\) is between \(0^{\circ}\) and \(90^{\circ}\). Label the vertex as \(I\) and the rays as \(\overrightarrow{IJ}\) and \(\overrightarrow{IH}\).

Step12: Analyze problem 11

To draw a right - angle \(\angle3\):
Draw a ray \(\overrightarrow{AB}\). Using a protractor, draw another ray \(\overrightarrow{AC}\) such that the measure of \(\angle BAC = 90^{\circ}\). Label the vertex as \(A\), the rays as \(\overrightarrow{AB}\) and \(\overrightarrow{AC}\), and the angle as \(\angle3\).

Step13: Analyze problem 12

To draw a straight angle \(\angle CDE\):
Draw a ray \(\overrightarrow{DC}\). Then, draw another ray \(\overrightarrow{DE}\) such that the two rays form a straight line. The measure of \(\angle CDE=180^{\circ}\). Label the vertex as \(D\) and the rays as \(\overrightarrow{DC}\) and \(\overrightarrow{DE}\).

Answer:

1. Vertex: \(M\), Sides: \(\overrightarrow{MN}\), \(\overrightarrow{ML}\), Four - way naming: \(\angle M\), \(\angle NML\), \(\angle LMN\)
2. Vertex: \(D\), Sides: \(\overrightarrow{DC}\), \(\overrightarrow{DE}\), Four - way naming: \(\angle D\), \(\angle CDE\), \(\angle EDC\)
3. Vertex: \(R\), Sides: \(\overrightarrow{RS}\), \(\overrightarrow{RQ}\), Four - way naming: \(\angle R\), \(\angle SRQ\), \(\angle QRS\)
4. Vertex: \(T\), Sides: \(\overrightarrow{TS}\), \(\overrightarrow{TU}\), Four - way naming: \(\angle T\), \(\angle STU\), \(\angle UTS\)
5. Vertex: \(D\), Sides: \(\overrightarrow{DE}\), \(\overrightarrow{DC}\), Four - way naming: \(\angle D\), \(\angle EDC\), \(\angle CDE\), \(\angle3\)
6. Vertex: \(F\), Sides: \(\overrightarrow{FG}\), \(\overrightarrow{FE}\), Four - way naming: \(\angle F\), \(\angle GFE\), \(\angle EFG\), \(\angle4\)
7. Vertex: \(F\), Sides: \(\overrightarrow{FE}\), \(\overrightarrow{FG}\), Four - way naming: \(\angle F\), \(\angle EFG\), \(\angle GFE\), \(\angle1\)
8. Vertex: \(I\), Sides: \(\overrightarrow{IJ}\), \(\overrightarrow{IH}\), Four - way naming: \(\angle I\), \(\angle JIH\), \(\angle HIJ\), \(\angle3\)
9. Draw a ray, then using a protractor, draw another ray to form an angle between \(90^{\circ}\) and \(180^{\circ}\) and label as \(\angle Y\)
10. Draw a ray, then using a protractor, draw another ray to form an angle between \(0^{\circ}\) and \(90^{\circ}\) and label as \(\angle JIH\)
11. Draw a ray, then using a protractor, draw another ray to form a \(90^{\circ}\) angle and label as \(\angle3\)
12. Draw a ray, then draw another ray to form a \(180^{\circ}\) angle and label as \(\angle CDE\)