Angle Classifications
Kimberly Hopkins
Jen Kershaw
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Printed: August 23, 2016
AUTHORS
Kimberly Hopkins
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Angle Classifications
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Angle Classifications
In this concept, you will learn about angle classifications.
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.
Classifying Angles
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.
A 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.
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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 180◦ . 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.
Examples
Example 1
Earlier, you were given a problem about 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.
Example 2
Is the following angle acute, obtuse, right or straight?
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Chapter 1. Angle Classifications
First, determine the angle’s relationship to 90 degrees.
Greater than 90
Then, name the angle.
Obtuse
The answer is an obtuse angle.
Example 3
Is the following angle acute, obtuse, right or straight?
First, determine the angle’s relationship to 90 degrees.
Less than 90
Then, name the angle.
Acute
The answer is acute angle.
Example 4
Is the following angle acute, obtuse, right or straight?
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First, determine the angle’s relationship to 90 degrees.
Equal to 90
Then, name the angle.
Right
The answer is a right angle.
Example 5
Is the following angle acute, obtuse, right or straight?
First, determine the angle’s relationship to 90 degrees.
Greater than 90
The, name the angle.
Obtuse
The answer is an obtuse angle.
Review
Classify each angle as acute, right, obtuse or straight.
1.
2.
3.
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Chapter 1. Angle Classifications
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8.
9.
10.
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12.
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15.
88◦
An angle measuring
An angle measuring 90◦
An angle measuring 180◦
An angle measuring 105◦
An angle measuring 118◦
An angle measuring 5◦
An angle measuring 17◦
An angle measuring 135◦
An angle measuring 75◦
An angle measuring 5◦
An angle measuring 15◦
Review (Answers)
To see the Review answers, open this PDF file and look for section 9.5.
Resources
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/167997
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