1. Using Angle Relationships
to Solve Problems

2. Notes: Solving problems using angle relationships
5/20/2013
Example 1: Find the value of x in the diagram.
37o x
These are vertical angles, or opposite angles made by intersecting lines.
Relationship: Vertical angles are equal in measure.
x = 37o

3. Example 2: Find the value of x in the diagram.
Relationship: Vertical angles are equal in measure.
2x = 120o
Solve equation for x.
x = 60o

4. Relationship: Vertical angles are equal in measure.
Example 3: Find the value of x in the diagram.
3x - 10
50o
Relationship: Vertical angles are equal in measure.
Solve equation for x.
3x – 10 = 50o
3x = 60
x = 20o

5. Example 4: Find the value of x in the diagram.
These are supplementary angles.
Relationship: Supplementary angles add to 180o.
x + 53o = 180o
Solve equation for x.
x = 127o

6. Example 5: Find the value of x in the diagram.
Relationship: Supplementary angles add to 180o.
10x + 80o = 180o
Solve equation for x.
10x = 100o
x = 10o

7. Example 6: Find the value of x in the diagram.
Relationship: Supplementary angles add to 180o.
Solve equation for x.
x + x + 48o = 180o
2x + 48o = 180o
2x = 132o
x = 66o

8. Example 7: Find the value of x in the diagram.
These are complementary angles.
Relationship: Complementary angles add to 90o.
x + 15o = 90o
Solve equation for x.
x = 75o

9. Example 8: Find the value of x in the diagram.
Relationship: Complementary angles add to 90o.
3x + 63o = 90o
Solve equation for x.
3x = 27
x = 9o

10. Example 9: Find the value of x in the diagram.
x + 16o x
Relationship: Complementary angles add to 90o.
x + x + 16o = 90o
Solve equation for x.
2x + 16o = 90o
2x = 74
x = 37o