9-2 Measuring and Classifying Angles California Standards Preparation for MG2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

Also covered: Prep for

MG2.3

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9-2 Measuring and Classifying Angles

Vocabulary

angle vertex acute angle right angle obtuse angle straight angle

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9-2 Measuring and Classifying Angles

An angle is formed by two rays with a common endpoint, called the vertex. An angle can be named by its vertex or by its vertex and a point from each ray. The middle point in the name should always be the vertex.

Angles are measured in degrees. Use the symbol ° to show degrees.

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9-2 Measuring and Classifying Angles Additional Example 1: Measuring an Angle with a Protractor Use a protractor to measure the angle.

F G H

• Place the center point of the protractor on the vertex of the angle.

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9-2 Measuring and Classifying Angles Additional Example 1 Continued Use a protractor to measure the angle.

F G H

• Place the protractor so that ray GH passes through the 0 ° mark.

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9-2 Measuring and Classifying Angles Additional Example 1 Continued Use a protractor to measure the angle.

F G H

• Using the scale that starts with 0 ° along ray GH, read the measure where ray GF crosses.

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9-2 Measuring and Classifying Angles Reading Math

m  FGH is read “the measure of angle FGH.”

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9-2 Measuring and Classifying Angles Additional Example 1 Continued Use a protractor to measure the angle.

F G H

• The measure of  FGH is 120 ° . Write this as m  FGH = 120 ° .

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9-2 Measuring and Classifying Angles Check It Out!

Example 1 Use a protractor to measure the angle.

G H I

• Place the center point of the protractor on the vertex of the angle.

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9-2 Measuring and Classifying Angles Check It Out!

Example 1 Continued Use a protractor to measure the angle.

G H I

• Place the protractor so that ray HI passes through the 0 ° mark.

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9-2 Measuring and Classifying Angles Check It Out!

Example 1 Continued Use a protractor to measure the angle.

G H I

• Using the scale that starts with 0 ° along ray HI, read the measure where ray HG crosses.

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9-2 Measuring and Classifying Angles Check It Out!

Example 1 Continued Use a protractor to measure the angle.

G H I

• The measure of  GHI is 70 ° . Write this as m  GHI = 70 ° .

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9-2 Measuring and Classifying Angles Additional Example 2: Drawing an Angle with a Protractor Use a protractor to draw an angle that measures 80°.

• Draw a ray on a sheet of paper.

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9-2 Measuring and Classifying Angles Additional Example 2 Continued Use a protractor to draw an angle that measures 80°.

• Place the center point of the protractor on the endpoint of the ray.

• Place the protractor so that the ray passes through the 0° mark.

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9-2 Measuring and Classifying Angles Additional Example 2 Continued Use a protractor to draw an angle that measures 80°.

• Make a mark at 80° above the scale on the protractor.

• Use a straightedge to draw a ray from the endpoint of the first ray through the mark you made at 80°.

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9-2 Measuring and Classifying Angles Check It Out!

Example 2 Use a protractor to draw an angle that measures 45°.

• Draw a ray on a sheet of paper.

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9-2 Measuring and Classifying Angles Check It Out!

Example 2 Continued Use a protractor to draw an angle that measures 45°.

• Place the center point of the protractor on the endpoint of the ray.

• Place the protractor so that the ray passes through the 0° mark.

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9-2 Measuring and Classifying Angles Check It Out!

Example 2 Continued Use a protractor to draw an angle that measures 45°.

• Make a mark at 45° above the scale on the protractor.

• Use a straightedge to draw a ray from the endpoint of the first ray through the mark you made at 45°.

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9-2 Measuring and Classifying Angles

An acute angle measures less than 90 ° .

A right angle measures exactly 90 ° .

Reading Math

Right angles are usually marked with a symbol.

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9-2 Measuring and Classifying Angles

An obtuse angle measures more than 90 ° and less than 180 ° .

A straight angle measures exactly 180 ° .

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9-2 Measuring and Classifying Angles Additional Example 3: Classifying Angles Classify each angle as acute, right, obtuse, or straight.

A.

B.

The angle measures less than 90°, so it is an acute angle.

The angle measures exactly 90°, so it is a right angle.

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9-2 Measuring and Classifying Angles Check It Out!

Example 3 Classify each angle as acute, right, obtuse, or straight.

A.

B.

The angle measures less than 90°, so it is an acute angle.

The angle measures exactly 180°, so it is a straight angle.

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9-2 Measuring and Classifying Angles Additional Example 4: Application A welder used this piece of metal on his project. Classify



X,



Y, and



Z.

 X right  Y obtuse  Z acute

The angle is marked as a right angle.

The angle measures more than 90° and less than 180°. The angle measures less than 90°.

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9-2 Measuring and Classifying Angles Check It Out!

Example 4 A metal jeweler used this piece of metal on her project. Classify



A,



B, and



D.

A D

 A obtuse

C

 B acute  D right

B

The angle measures more than 90° and less than 180°. The angle measures less than 90°.

The angle is marked as a right angle.

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