Definition: Vertical angles are the pair of opposite angles formed when two lines cross, and they always have equal measures.
What are vertical angles?
When two straight lines intersect, they form four angles. The angles directly across from each other are vertical angles. They share a vertex but no side.
What is the key fact?
Vertical angles are congruent. If one measures 64 degrees, the angle across from it also measures 64 degrees.
Why is it true?
Each of the other two angles is supplementary to both. So both vertical angles equal 180 minus the same angle.
How do you solve a problem?
Two crossing lines make angles of (5x – 8) degrees and (3x + 22) degrees as a vertical pair. Set them equal: 5x – 8 = 3x + 22, so 2x = 30 and x = 15. Each angle is 5(15) – 8 = 67 degrees. The other two angles are 180 – 67 = 113 degrees each.
What is a common mistake?
Thinking that any two angles at a crossing are equal. Only the opposite ones are. Neighbors along a line are supplementary and add to 180 degrees.