Mathematics 4 Life and Beyond: Classifying Angles (8-2)

Classifying Angles

Vocabulary

Angle- formed by two rays and one common endpoint.

Vertex- the common endpoint.

Right Angle- an angle that measures exactly 90 degrees.

Acute Angle- an angle that measures greater than 0 but less than 90 degrees.

Obtuse Angle- an angle that measures more than 90 but less than 180 degrees.

Straight Angle- this angle measures exactly 180 degrees.

Complimentary Angle- the sum of two angles measuring 90 degrees.

Supplementary Angle- the sum of two angles measuring 180 degrees.

Examples

If you look around you, you'll see angles everywhere. Angles are measured in degrees

. A degree is a fraction of a circle—there are 360 degrees in a circle, represented like this: 360�.
You can think of a right angle as one-fourth of a circle, which is 360� divided by 4, or 90�.
The right angle is the most common angle—the edges of your notebook paper, stair steps

, door facings, the edges of picture frames—all of these form right angles. Let's look at some other types of angles. A straight angle represents half of a circle. 360� divided by 2 equals 180�—that is the measure of a straight angle. An acute angle is any angle that measures less than 90�. An obtuse angle measures greater than 90� but less than 180�.
We can estimate angle measures by looking at them and comparing them mentally with angles we know, such as the right angle. But how do we measure angles exactly?

This useful tool is called a protractor, and any student of geometry should have one! It is used both to measure angles and to draw angles. To use a protractor, place the arrow on the vertex of the angle you want to measure, and read off the measurement on the scale, in degrees

.
Two angles that have the same measure are called congruent angles.

Here are two angles that both measure 30�. We say that angle x is congruent to angle y.
Now let's look at some angle pairs. Two angles are called supplementary if their measures add up to 180�. These two 90� angles are supplementary because 90 + 90 = 180.