Geometry and Solid Figures: Parallel lines and Transversals

-  When a line (transversal) intersects two parallel lines in the same plane, eight angles are formed.

In the following diagram, a transversal intersects two parallel lines. Angles 1, 3, 5, and 7 are congruent.

Angles 2, 4, 6, and 8 are also congruent.
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In the following diagram, the following angles are supplementary angles (their sum is 180):

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

Example:

In the following diagram, two parallel lines are cut by a transversal. What is the value of ?
Solution: The two angles and are equivalent.
That is:
Now, solve for :