Angle Relationships
Overview
Pairs of angles have names based on how their measures combine and where they sit. Complementary angles total 90° and supplementary angles total 180°. Adjacent angles share a vertex and a side; vertical angles sit opposite each other where two lines intersect and are always congruent; a linear pair is both adjacent and supplementary. Perpendicular lines are the special case of intersecting lines that form right angles.
Vocabulary
- Complementary Angles
- Any two angles whose measures total 90°. Each angle is the complement of the other.
- Supplementary Angles
- Any two angles whose measures total 180°. Each angle is the supplement of the other.
- Adjacent Angles
- Two angles that share a vertex and one common side, with no interior points in common — they are next to each other with no gaps and no overlap.
- Vertical Angles
- Two non-adjacent angles formed by two intersecting lines, opposite each other at the intersection. Vertical angles are congruent.
- Linear Pair
- A pair of angles that are both adjacent and supplementary. The measures of a linear pair total 180°.
- Perpendicular Lines
- Lines that intersect to form right angles. A small square drawn at the vertex marks a right angle in a figure.
- Right Angle
- An angle whose measure is 90°.
Main Ideas
- Complementary means the measures add to 90°; supplementary means the measures add to 180°. The names describe the sum, not the positions — neither pair has to be adjacent.
- Vertical angles are congruent: set their measures equal. They are never adjacent.
- A linear pair is supplementary by definition, because the two angles together form a straight angle.
- Chain the relationships: find one angle from a pair, then use that result in the next relationship.
- After solving for x, substitute back and classify or report the measure asked for — algebra answers and angle measures are different things.
Lesson Notes
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Lesson Video
Watch the lesson video.
Interactive Activity
Work with complementary, supplementary, vertical, and adjacent angles and the relationships between them.
Practice Problems
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Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.