Find measures of complementary, supplementary, vertical, and adjacent angles

Learning Objectives Define and identify complementary, supplementary, vertical, and adjacent angles in a diagram. Formulate algebraic equations based on the relationships between angle pairs. Solve for unknown angle measures by applying the properties of complementary and supplementary angles. Solve for unknown angle measures using the Vertical Angles Theorem. Distinguish between adjacent angles and a linear pair. Solve multi-step problems that combine multiple angle pair relationships. Ever noticed how the streets on a city map intersect to form different angles? 🗺️ The relationships between those angles are critical for everything from navigation to architecture! This tutorial will explore four fundamental angle relationships: complementary, supplementary, vertical, and a...

TermDefinitionExample Adjacent AnglesTwo angles that share a common vertex and a common side, but have no common interior points. They are 'next to' each other.In a diagram where ray OB extends from the vertex O between the rays OA and OC, ∠AOB and ∠BOC are adjacent angles. Complementary AnglesTwo angles whose measures have a sum of 90 degrees. They do not have to be adjacent.A 30° angle and a 60° angle are complementary because 30° + 60° = 90°. Supplementary AnglesTwo angles whose measures have a sum of 180 degrees. They do not have to be adjacent.A 110° angle and a 70° angle are supplementary because 110° + 70° = 180°. Linear PairA pair of adjacent angles whose non-common sides are opposite rays (form a straight line). Angles in a linear pair are always supplementary.If two an...

Complementary Angles Sum If ∠A and ∠B are complementary, then m∠A + m∠B = 90° Use this rule when you are given that two angles are complementary or when they form a right angle. Set the sum of their measures equal to 90 to find an unknown value. Supplementary Angles Sum / Linear Pair Postulate If ∠A and ∠B are supplementary, then m∠A + m∠B = 180° Use this rule when you are told two angles are supplementary or when they form a linear pair (a straight line). Set the sum of their measures equal to 180. Vertical Angles Theorem If ∠A and ∠C are vertical angles, then m∠A = m∠C (or ∠A ≅ ∠C) Use this theorem when you have two intersecting lines. Set the measures of the angles opposite each other at the intersection point equal to each other.