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# Angle Classification

## Categories of angles based on measurements and relationships.

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Angle Classification

Claire's art teacher gave her an image and asked her to make a painting that recreates the image. Claire likes to paint general shapes as her starting points and then draws in more details later. The first shape that she notices is the hat on the woman's head. She sees that the hat looks like an angle. If Claire recreates the angle on her painting, will she have a right angle, straight angle, acute angle or an obtuse angle?

In this concept, you will learn about angle classifications.

### Guidance

An angle is formed when two rays connect at a single endpoint. You can measure an angle in degrees. When measuring an angle, you are measuring the space between the two rays.

The arc represents the space of the angle that you are measuring. This angle is very small as you can see by the size of the arc.

This arc is very large. The space between the rays is large so the angle is large too.

You can classify or organize angles according to the size of the angle. The size of the angle is classified according to the number of degrees.

There are 4 major types of angles.

right angle is an angle that is exactly 90 degrees. It is easy to recognize because it forms a corner that is straight. Often with a right angle you will see a little box in the corner too.

An acute angle is an angle that is greater than 0 degrees but less than 90 degrees. Here is an example of an acute angle.

A straight angle is the same as a straight line. A straight line is equal to \begin{align*}180^\circ\end{align*}. The angle of a straight line stretches from one side of the line to the other side as indicated by the arc in this picture.

An obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees. Here is an example of an obtuse angle.

### Guided Practice

Is the following angle acute, obtuse, right or straight?

First, determine the angle's relationship to 90 degrees.

Greater than 90

Then, name the angle.

Obtuse

The answer is an obtuse angle.

### Examples

Identify the following angles as acute, obtuse, right or straight.

#### Example 1

First, determine the angle's relationship to 90 degrees.

Less than 90

Then, name the angle.

Acute

#### Example 2

First, determine the angle's relationship to 90 degrees.

Equal to 90

Then, name the angle.

Right

The answer is a right angle.

#### Example 3

First, determine the angle's relationship to 90 degrees.

Greater than 90

The, name the angle.

Obtuse

The answer is an obtuse angle.

Remember Claire and her painting? Claire sees the angle of the woman's hat. Look at the top point of the hat and the angle as the hat moves down to her head.  Is the angle a right angle, straight angle, acute angle or an obtuse angle?

First, determine the angle's relationship to 90 degrees.

Less than 90

Then, name the angle.

Acute

The answer is acute angle. The hat looks like an acute angle.

### Explore More

Classify each angle as acute, right, obtuse or straight.

1.

2.

3.

4.

5. An angle measuring \begin{align*}88^\circ\end{align*}

6. An angle measuring \begin{align*}90^\circ\end{align*}

7. An angle measuring \begin{align*}180^\circ\end{align*}

8. An angle measuring \begin{align*}105^\circ\end{align*}

9. An angle measuring \begin{align*}118^\circ\end{align*}

10. An angle measuring \begin{align*}5^\circ\end{align*}

11. An angle measuring \begin{align*}17^\circ\end{align*}

12. An angle measuring \begin{align*}135^\circ\end{align*}

13. An angle measuring \begin{align*}75^\circ\end{align*}

14. An angle measuring \begin{align*}5^\circ\end{align*}

15. An angle measuring \begin{align*}15^\circ\end{align*}

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 9.5.

### Vocabulary Language: English

Acute Angle

An acute angle is an angle with a measure of less than 90 degrees.

Obtuse angle

An obtuse angle is an angle greater than 90 degrees but less than 180 degrees.

Perpendicular

Perpendicular lines are lines that intersect at a $90^{\circ}$ angle. The product of the slopes of two perpendicular lines is -1.

Right Angle

A right angle is an angle equal to 90 degrees.

Straight angle

A straight angle is a straight line equal to $180^{\circ}$.