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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

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 D E 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 D E 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 D E 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 D E 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 D E 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!