### Relationship

```Example 1: Find the value of x in the diagram.
37o
x
These are vertical angles, or opposite
Relationship:
Vertical angles are equal in measure.
x = 37o
Example 2: Find the value of x in the diagram.
120o
2x
Relationship:
Vertical angles are equal in measure.
Solve equation for x.
2x = 120o
2
2
x = 60o
Example 3: Find the value of x in the diagram.
3x - 10
50o
Solve equation for x.
Relationship:
Vertical angles are
equal in measure.
3x – 10 = 50o
+ 10 +10
3x
3
= 60
3
x = 20o
Example 4: Find the value of x in the diagram.
x
53o
These are supplementary angles.
Relationship:
Solve equation for x.
x + 53o = 180o
- 53 - 53
x
= 127o
Example 5: Find the value of x in the diagram.
10x
80o
Relationship:
Solve equation for x.
10x + 80o = 180o
- 80 - 80
10x
10
= 100o
10
x = 10o
Example 6: Find the value of x in the diagram.
x
x + 48
Relationship:
Solve equation for x.
x + x + 48o = 180o
2x + 48o = 180o
- 48 - 48
2x = 132o
2
2
x = 66o
Example 7: Find the value of x in the diagram.
x
15o
These are complementary angles.
Relationship:
Solve equation for x.
x + 15o = 90o
- 15 - 15
x
= 75o
Example 8: Find the value of x in the diagram.
63o
3x
Solve equation for x.
Relationship:
3x + 63o = 90o
- 63 - 63
3x
= 27
3
3
x = 9o
Example 9: Find the value of x in the diagram.
x + 16o
x
Relationship: