This document provides instructions for determining angle measures when parallel lines are cut by a transversal. It defines key terms like parallel lines, transversal, and corresponding angles. It explains properties of angles like supplementary angles that add to 180 degrees and vertical angles that are equal. Examples show how to use these properties to find missing angle measures, such as if one corresponding angle is known, the other equal angle can be determined without a protractor.

1. Determining Angle
Measures when
Parallel Lines Are Cut
by a Transversal
Today’s Lesson

2. Warm-Up Activity
We will warm up today
by finding angle
measures.

3. These are supplementary angles.
150°x
How can you find the missing angle
without using a protractor?
Supplementary angles add up to 180°.

4. x + 150 = 180
150°x
The supplementary angles add up to
180 degrees.
30°
x = 180 – 150
x = 30

5. 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°

6. 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.

7. 82°
32°x
The sum of the
triangle’s angles
equals 180
degrees.
82 + 32 + x = 180
114 + x = 180
x = 180 – 114
x = 66
66°

8. Today, you will focus on
using patterns to find
missing angles.
Whole-Class Skills Lesson

9. Congruent Angles
have the same measure in degrees
43°
43°

10. Parallel Lines
Are always the same distance apart.
They will never intersect.

11. Transversal
A line that crosses a pair of parallel lines.

12. Corresponding Angles
Angles in the same position on parallel
lines cut by a transversal are congruent.
1
2
34
A
B
CD

13. Corresponding Angles
1
2
34
A
B
CD
1∠≅∠A
2∠≅∠B
3∠≅∠C
4∠≅∠D

14. Supplementary angles add
up to 180 degrees.
Vertical angles have the
same angle measure.
The sum of the triangle’s
angles equals 180 degrees.

15. 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

16. Lines a and b are parallel.
a
b
c
1 2
34
5
78
6
Can you name the corresponding angles?
Angles 1 and 5
Angles 4 and 8
Angles 2 and 6
Angles 3 and 7

17. Lines a and b are parallel.
a
b
c
1 2
34
5
78
6
Can you name the vertical angles?
Angles 1 and 3
Angles 4 and 2
Angles 5 and 7
Angles 6 and 8

18. 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 2
Angles 2 and 3
Angles 3 and 4
Angles 4 and 1
Angles 5 and 6
Angles 6 and 7
Angles 7 and 8
Angles 5 and 8

19. 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°

20. 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°

21. 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°

22. 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°

23. 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°

24. 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°