1.2b Angle Pairs
LEARNING OBJECTIVES
- Describe complementary, supplementary, adjacent, linear pair, and vertical angles.
- Explain the relationships between these angle pairs.
Review
Before we proceed, let’s quickly review what an angle is.
What is an Angle?
An angle is formed by two rays that meet at a common endpoint called the vertex.
To help you recall the parts of an angle, try doing the activity below.
Angle Pairs
Now that you’ve recalled what an angle is, let’s move on to learning about angle pairs. These are pairs of angles that have special relationships. These include complementary angles, supplementary angles, adjacent angles, linear pairs, and vertical angles.
Complementary Angles
Complementary Angles
Definition: Two angles are complementary if the sum of their measures is exactly 90°.
Example: If one angle measures 30°, its complementary must measure 60° since (30° + 60° = 90°).
Supplementary Angles
Supplementary Angles
Definition: Two angles are supplementary if the sum of their measures is exactly 180°.
Example: If one angle measures 110°, its supplementary must measure 70° since (110° + 70° = 180°).
Explore this interactive illustration of complementary and supplementary angles. Move point to change the size of the angle.
Adjacent Angles
Adjacent Angles
Definition: Adjacent angles are two angles that share a common side and vertex but do not overlap.
Example: See the interactive illustration below.
Linear Pair
Linear Pair
Definition: A linear pair is a pair of adjacent angles that form a straight line. Together, these angles add up to 180°.
Example: When two lines intersect, they create adjacent angles that are linear pairs. If one angle measures 120°, the other in the pair will measure 60°.
Vertical Angles
Vertical Angles
Definition: Vertical angles are pairs of opposite angles formed when two lines intersect. These angles are always equal in measure.
Example: See interactive illustration below.
Interact with the illustration below to visualize linear pair and vertical angles.
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