Angel Relationships Cheat Sheet

Understand the fundamental relationships between angles, including adjacent, vertical, complementary, supplementary, and linear pairs, to solve geometric problems.

Core Principles

• Angles share a common vertex and ray (adjacent).
• Vertical angles are opposite and equal.
• Complementary angles sum to 90°.
• Supplementary angles sum to 180°.
• Linear pairs form a straight line (180°).

Key Terms

• Angle: The figure formed by two rays sharing a common endpoint (vertex).
• Vertex: The common endpoint of the two rays forming an angle.
• Adjacent Angles: Angles that share a common vertex and a common side, but do not overlap.
• Vertical Angles: Pairs of opposite angles formed by the intersection of two lines. They are always congruent.
• Complementary Angles: Two angles whose measures add up to 90 degrees.
• Supplementary Angles: Two angles whose measures add up to 180 degrees.
• Linear Pair: A pair of adjacent angles whose non-common sides form a straight line (180 degrees).

Real World Examples

• Clock hands at 3:00: The angle between the hour and minute hands is often a right angle (90°), related to complementary angles.
• A straight road intersection: Angles formed at the intersection can be vertical pairs (equal) or supplementary (add to 180°).
• Corner of a book: Forms a right angle (90°), a basis for understanding complementary angles.
• A flat horizon line: Represents a straight angle (180°), fundamental to supplementary angles and linear pairs.

Quiz

• If two angles are complementary and one measures 30°, what is the measure of the other?: 60°
• Vertical angles are always:: Equal
• A linear pair of angles always adds up to:: 180°