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What are angles?

An angle is formed by 2 lines or rays diverging from a common point (known as the vertex.)

Two rays

< Vertex

Classifying Angles

Classifying and Measuring Angles

Angles are measured in degrees. Angles can be classified based on their measurement. There are 4 main classification “groups” for angles.

The Acute Angle

Acute angles are angles that measure less than 90°.

An acute angle

The Obtuse Angle

Obtuse angles measure more than 90°.

An obtuse angle

The Right Angle

A right angle is a special type of angle, since right angles can only have one measurement, and that is 90°.

A right angle

< This little square here indicates that this angle is a

right angle.

The Straight Angle

A straight angle is a another special type of angle, since it also can only have one measurement, and that is 180°.

A straight angle

Naming Angles

Naming Angles

Besides classifying angles, you can also name them according to the labels they’re given.

Example of Naming Angles

This right angle has been labeled in 4 different spots: one on the interior near the vertex, one on the exterior near the vertex, and two near the ends of the rays.

C

DE

3

Example of Naming Angles

We can name this angle in 4 different ways: ∠ CDE, EDC, D, and 3.∠ ∠ ∠

But how do they get those names?C

DE

3

Example of Naming Angles

Both of the names CDE and EDC are acquired ∠ ∠from the labels for the vertex and ends of the rays. If using this method of naming, make sure that the vertex label (in this case, D) is in the middle of the name! C

DE

3

Example of Naming Angles

The other two names, D and 3, are acquired from ∠ ∠the labels of the vertex alone. The name D is taken ∠from the exterior vertex label, while 3 is taken from ∠the interior vertex label.

C

DE

3

Naming Angles

If you remember the 2 different methods for naming angles (when given the 4 labels shown below), you will be able to accurately and correctly name angles.

C

DE

3

Complimentary and Supplementary Angles

Complimentary Angles

Complimentary angles are simply angles that add up to 90°.

An example of complimentary angles

Complimentary Angles

If you know that 2 angles are complimentary, you can easily figure out the measures of both angles (if the measurement of 1 has been given.)

Complimentary Angles

For example, if you know that one angle is 67°, you can easily find out the measure of the second angle by simply subtracting that 67 from 90 (the total measurement of both angles together.)

67°

After subtracting 67 from 90, we can find that the

measurement of the other angle is 23°.

Supplementary Angles

Similarly, supplementary angles are angles that add up to 180°.

An example of supplementary angles

Supplementary Angles

So, if you know that 2 angles are supplementary, you can easily figure out the measures of both angles (if the measurement of 1 has been given.)

Supplementary Angles

For example, if you know that one angle is 52°, you can easily find out the measure of the second angle by simply subtracting that 52 from 180 (the total measurement of both angles together.)

52°

After subtracting 52 from 180, we can find that the

measurement of the other angle is 128°.

Review/ Practice

Review

Answer the following questions.What is an angle (by what is it formed)?An angle is formed by 2 lines or rays diverging from a common point (known as the vertex.)

Review

Answer the following questions.What is an acute angle?An acute angle is an angle that measures less than 90°.What is an obtuse angle?An obtuse angle is an angle that measures more than 90°.

Review

Answer the following questions.What is a right angle?A right angle is an angle that measures exactly 90°.What is a straight angle?A straight angle is an angle that measures exactly 180°.

Review

Answer the following questions.What are complimentary angles?Complimentary angles are angles that add up to 90°.What are supplementary angles?Supplementary angles are angles that add up to 180°.

Practice

Classify the following angles.

Right angle

Practice

Classify the following angles.

Acute angle

Practice

Classify the following angles.

Obtuse angle

Practice

Classify the following angles.

Acute angle

Practice

Classify the following angles.

Right angle

Practice

Classify the following angles.

Straight angle

Practice

Classify the following angles.

Obtuse angle

Practice

Name the following angles. (There are 4 possible answers.)

∠ ABC, CBA, B, 1∠ ∠ ∠

A B

C

1

Practice

Name the following angles. (There are 4 possible answers.)

∠ QRS, SRQ, R, 6∠ ∠ ∠

Q R

S

6

Practice

Name the following angles. (There are 4 possible answers.)

∠ GHI, IHG, H, 8∠ ∠ ∠

G H

I

8

Practice

Find the measure of angle b.

∠b= 58° 32°b

Practice

Find the measure of angle b.

∠b= 116° 64° b

Practice

Find the measure of angle b.

∠b= 14°

76°

b

Practice

Find the measure of angle b.

∠b= 48° 42°

b

Practice

Find the measure of angle b.

∠b= 55° 125° b

Congratulations

You now know a lot about angles!