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Determining Angle Measures when Parallel Lines Are Cut

by a Transversal

Today’s Lesson

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Warm-Up Activity

We will warm up today by finding angle measures.

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These are supplementary angles.

150°x

How can you find the missing angle without using a protractor?

Supplementary angles add up to 180°.

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x + 150 = 180

150°x

The supplementary angles add up to 180 degrees.

30°

x = 180 – 150 x = 30

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43°x

How can you find the missing angle without using a protractor?

These angles are vertical. Vertical angles have the same angle measure.

x = 43°

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82°

32°x

How can you find the

missing angle of the

triangle without using a protractor?What do you know about

triangles that will help you find the missing angle?

The sum of the triangle’s angles equals 180 degrees.

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82°

32°x

The sum of the

triangle’s angles

equals 180 degrees.82 + 32 + x = 180

114 + x = 180x = 180 – 114

x = 66

66°

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Today, you will focus on using patterns to find missing angles.

Whole-Class Skills Lesson

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Congruent Angles

have the same measure in degrees

43° 43°

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Parallel Lines

Are always the same distance apart.

They will never intersect.

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Transversal

A line that crosses a pair of parallel lines.

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Corresponding Angles

Angles in the same position on parallel lines cut by a transversal are congruent.

12

34

AB

CD

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Corresponding Angles1

2

34

AB

CD1A2B3C4D

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Supplementary angles add up to

180 degrees.

Vertical angles have the same angle measure.

The sum of the triangle’s angles

equals 180 degrees.

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Lines a and b are parallel.

a

b

c

1 2

34

5

78

6

What types of angles do you see in this example?

Supplementary, Vertical, and Corresponding Angles

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Lines a and b are parallel.

a

b

c

1 2

34

5

78

6

Can you name the corresponding angles?

Angles 1 and 5Angles 4 and 8Angles 2 and 6Angles 3 and 7

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Lines a and b are parallel.

a

b

c

1 2

34

5

78

6

Can you name the vertical angles?

Angles 1 and 3Angles 4 and 2Angles 5 and 7Angles 6 and 8

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Lines a and b are parallel.

a

b

c

1 2

34

5

78

6

Can you name some of the supplementary angles?

Angles 1 and 2Angles 2 and 3Angles 3 and 4Angles 4 and 1

Angles 5 and 6Angles 6 and 7Angles 7 and 8Angles 5 and 8

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Lines a and b are parallel.

a

b

c

110 2

34

5

78

6

If Angle 1 measures 110 degrees, what is the measure of Angle 3?

110°

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Lines a and b are parallel.

a

b

c

110 2

34

5

78

6

If Angle 1 measures 110 degrees, what is the measure of Angle 4?

70°

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Lines a and b are parallel.

a

b

c

110 2

34

5

78

6

If Angle 1 measures 110 degrees, what is the measure of Angle 8?

70°

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Lines a and b are parallel.

a

b

c

110 2

34

5

78

6

If Angle 1 measures 110 degrees, what is the measure of Angle 7?

110°

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Lines a and b are parallel.

a

b

c

1 2

34

5

78

52°

If Angle 6 measures 52 degrees, what is the measure of Angle 7?

128°

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Lines a and b are parallel.

a

b

c

1 2

34

5

78

52°

If Angle 6 measures 52 degrees, what is the measure of all the angles on the diagram?

128°

128° 52°

52°

128°

52° 128°