Solving Problems Involving Parallel Lines
Completion requirements
C. Solving Problems Involving Parallel Lines
You can now use the angle relationships you have learned to determine unknown angles in more complex figures that include parallel lines. When solving problems involving angle measurements, it is a good idea to add the measure of each angle you determine to the diagram. This will aid you in determining other angle measures. Sometimes you will need to find the measure of angles you are not directly asked to find so that their measures can assist you in finding the desired ones.
Example 1
Determine all the unknown angles in the diagram.
Each time you determine a new angle measure, you can use that information to help determine other angles. The following table represents a possible method of determining the unknown angles in the diagram.
| Angle Measurement | Reason | Diagram |
|---|---|---|
| ∠GFI = 36° | ∠GFI and ∠I are alternate interior angles |  |
| ∠BFE = 36° | ∠GFI and ∠BFE are opposite angles | |
| ∠EFI = 144° | ∠GFI and ∠EFI form a straight line and so they are supplementary (they add to 180°) | |
| ∠BFG = 144° | ∠EFI and ∠BFG are opposite angles | |
| ∠CBF = 36° | ∠GFI and ∠CBF are corresponding angles | |
| ∠DEH = 49° | ∠H and ∠DEH are alternate interior angles |  |
| ∠BEF = 49° | ∠DEH and ∠BEF are opposite angles | |
| ∠BED = 131° | ∠BEF and ∠BED form a straight line and so they are supplementary | |
| ∠FEH = 131° | ∠BED and ∠FEH are opposite angles | |
| ∠ABE = 49° | ∠DEH and ∠ABE are corresponding angles | |
| ∠EBF = 95° | ∠ABE, ∠CBF, and ∠EBF form a straight line so sum to 180° |  |
