Here are the steps: 1. Identify the relationship between the angles. 2. Write the appropriate equation based on the relationship: - Equal relationships (vertical, alternate interior, etc.): Angle = Angle - Supplementary relationships: Angle + Angle = 180 3. Solve the equation for x. 4. Substitute back into the original angles to find the missing measures. Let's practice a few examples together. Then you can work through some on your own.

1. Ms. Johnson 8th Grade math

2.  Parallel
lines: Lines that are the same
distance apart over their entire length

3.  Parallel
lines: Lines that are the same
distance apart over their entire length
Transversal: a line that crosses two other lines

4.  Parallel
lines: Lines that are the same
distance apart over their entire length
Transversal: a line that crosses two other lines

5.  When you have a transversal cutting across
parallel lines certain relationships are
formed

6. Lines l and m are parallel.
l||m
Note the 4
angles that
measure
120°.
120°
120°
l
120°
120° m
Line n is a transversal.
n

7. Lines l and m are parallel.
l||m
Note the 4
angles that
measure 60°.
60°
60°
l
60°
60° m
Line n is a transversal.
n

8. Lines l and m are parallel.
l||m
There are many There are 4 pairs of
pairs of angles that angles that are
are supplementary. vertical.
60°
120°
120°
60°
l
60° 120°
120° 60° m
Line n is a transversal.
n

9. Practice Time!

10. 9) Lines l and m are parallel.
l||m
Find the missing angles.
42°
a°
c°
b°
l
d° e°
g° f° m

11. 9) Lines l and m are parallel.
l||m
Find the missing angles.
42°
138°
138°
42°
l
42° 138°
138° 42° m

12. 10) Lines l and m are parallel.
l||m
Find the missing angles.
81°
a°
c°
b°
l
d° e°
g° f° m

13. 10) Lines l and m are parallel.
l||m
Find the missing angles.
81°
99°
99°
81°
l
81° 99°
99° 81° m

14.  Sowe know that given a transversal cutting 2
parallel lines, certain relationships are
formed. Some of the angles are
supplementary because they are on a
straight line. And some angles are vertical
and thus equal.

15. But in this picture, how did we know that the
angles highlighted in red are the same????
120°
120°
l
120°
120° m
Line n is a transversal.
n

16.  We knew because there are angle
relationships of equality besides the vertical
angle theorem..
 Congruent Angle Relationships (=):
Vertical
Alternate Interior (AI)
Alternate Exterior (AE)
Corresponding

17.  We knew because there are angle
relationships of equality besides the vertical
angle theorem..
 Congruent Angle Relationships (=):
Vertical
Alternate Interior (AI)
Alternate Exterior (AE)
Corresponding
 Ifthe angles in the scenario are not equal to
each other, then they are supplementary!!

18. The easiest way to see these relationships: Imagine a sandwich.
The parallel lines are the bread.
The transversal is the toothpick.

19. Vertical angles: are on the same slice of “bread” on
different sides of the “toothpick.”

20. Alternate Interior angles: are inside the “bread”, on opposite sides
of the “toothpick.”

21. Alternate Interior angles: are inside the “bread”, on opposite sides
of the “toothpick.”
Alternate Exterior angles: are outside the “bread,” on opposite sides
of the “toothpick.”

22. Corresponding angles: are on different slices of “bread,” on the same
side of the toothpick.
Angles are in the same position (both are
top left, top right, bottom left, or bottom right).
It’s almost like you put one slice of bread
on top of the other.

23.  We actually already know how to find the missing angle
using algebra.
 First, identify the relationship.

24.  We actually already know how to find the missing angle
using algebra.
 First, identify the relationship.
 Second, write the equation. If it’s any of these:
Vertical (V)
Alternate exterior (AE)
Alternate interior (AI)
Corresponding (C)
Then use the same equation you do for all equal
relationships. Angle = Angle (the sneaker)
And solve for x. Substitute if necessary.

25.  We actually already know how to find the missing angle
using algebra.
 First, identify the relationship.
 Second, write the equation. If it’s NOT any of these:
Vertical (V)
Alternate exterior (AE)
Alternate interior (AI)
Corresponding (C)
Then the relationship has to be supplementary, so the
equation is Angle + Angle = 180 (“the boot”)
And solve for x. Substitute if necessary.

26. Use Algebra to Find Missing Angles
Ex. 1
Find x and the unknown angle.
120°
(2x)°

27. Find x and the unknown angle.
120°
(2x)°
First, we identify the relationship:

28. Find x and the unknown angle.
120°
(2x)°
First, we identify the relationship:
Alternate Interior

29. Find x and the unknown angle.
120°
(2x)°
First, we identify the relationship:
Alternate Interior
which means the angles are congruent (=)

30. Find x and the unknown angle.
120°
(2x)°
2x = 120

31. Find x and the unknown angle.
120°
(2x)°
2x = 120
2 2

32. Find x and the unknown angle.
120°
(2x)°
2x = 120
• 2
x = 60

33. Find x and the unknown angle.
120°
(2x)°
Now to find the unknown angle, we can just substitute back in.
We need to find what angle 2x equals….. 2(60) = 120
So the unknown angle is 120°

34. Example 2
Find x and the unknown angle.
2x + 20
70°

35. Example 2
Find x and the unknown angle.
2x + 20
70°
First we identify the relationship.

36. Example 2
Find x and the unknown angle.
2x + 20
70°
First we identify the relationship.
Corresponding

37. Example 2
Find x and the unknown angle.
2x + 20
70°
First we identify the relationship.
Corresponding
So angle = angle

38. Example 2
Find x and the unknown angle.
2x + 20
70°
Corresponding
2x + 20 = 70

39. Example 2
Find x and the unknown angle.
2x + 20
70°
Corresponding
2x + 20 = 70
-20 -20
2x = 50

40. Example 2
Find x and the unknown angle.
2x + 20
70°
Corresponding
2x + 20 = 70
-20 -20
2x = 50
2 2

41. Example 2
Find x and the unknown angle.
2x + 20
Corresponding
70°
2x + 20 = 70
-20 -20
2x = 50
• 2
x = 25

42. Example 2
Find x and the unknown angle.
2x + 20
Now we 70°
substitute
back in.
2(25) + 20 =

43. Example 2
Find x and the unknown angle.
2x + 20
Now we substitute 70°
back in.
2(25) + 20 = 70
So the missing angle
is 70°

44. Example 2
Find x and the unknown angle.
(3x + 30)°
(2x + 40)°

45. Example 2
Find x and the unknown angle.
(3x + 30)°
Find the relationship.
(2x + 40)°

46. Example 2
Find x and the unknown angle.
(3x + 30)°
Find the relationship. These
angles are supplementary. So (2x + 40)°
angle + angle = 180

47. Example 2
Find x and the unknown angle.
(3x + 30)°
Supplementary
3x + 30 (2x + 40)°
2x + 40
= 180

48. Example 2
Find x and the unknown angle.
(3x + 30)°
Supplementary
3x + 30 (2x + 40)°
2x + 40
5x + 70 = 180

49. Example 2
Find x and the unknown angle.
(3x + 30)°
Supplementary
3x + 30 (2x + 40)°
2x + 40
5x + 70 = 180
-70 -70
5x = 110

50. Example 2
Find x and the unknown angle.
(3x + 30)°
Supplementary
3x + 30
2x + 40
5x + 70 = 180
-70 -70 (2x + 40)°
5x = 110
• 5
x = 22

51. Example 2
Find x and the unknown angle.
(3x + 30)°
Supplementary
x = 22
Now substitute into angles:
(2x + 40)°
3(22) + 30 = 96
2(22) + 40 = 84

52. ACTIVITY
Green cards: Name the relationship. Write about how you identified
the relationship. Use 2-Step Equations to find
x and the missing angle.
Pink cards: Name the relationship. Write about how you identified
the relationship. Use Multi-Step Equations to find
x and the missing angles.