Angle Relationships
There are many types of angle relationships, such as complementary and supplementary angles - 2 angles that make 90° (complementary) or 180° (supplementary). There are many different types of angle relationships such as:
- Congruent: Two angles that have the same measurement
- Adjacent: 2 angles that share a vertex and a side
- Interior and Exterior: (below)
- Vertical: 2 angles across from each other that share a vertex and are made from the same 2 lines. These angles are always congruent.
Angles 1, 2, 7, and 8 would be exterior angles because they are outside of the parallel lines. Angles 3, 4, 5, and 6 would be interior angles because they are inside of the parallel lines.
Angles 1 and 8 would be alternate exterior angles because the horizontal lines are parallel and are outside, or exterior to the horizontal lines. Angles 2 and 7 would also be alternate exterior angles. Angles 3 and 6 would be alternate interior angles because they are on the inside or interior side of the horizontal lines. Angles 4 and 5 are alternate interior angles as well. The alternate angles will be on different sides of the transversal.
- Alternate Exterior and Interior: (above) Angles related in this way will always be congruent.
Complementary Angles Example
![Picture](/uploads/1/9/8/7/19872907/151141659.gif)
- In the bottom left corner, you see there is a square/rectangle. That means the full angle is 90 degrees. This is where our complementary angles solving skill comes in!
- The angle on top is 60 degrees. and since the whole angle is 90 degrees, subtract 60 degrees from 90 degrees and you get 30 degrees - 90-60=30.
- Angle x would be 30 degrees.
Alternate Interior/Supplementary Angles Practice Problem
![Picture](/uploads/1/9/8/7/19872907/770821085.gif)
1. Given that angle 3 is 117 degrees, what is the measurement of angle 6?
2. What angles are congruent to angle 2, and how many are there?
Answer Key
2. What angles are congruent to angle 2, and how many are there?
Answer Key