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

Learning Objectives Define and identify complementary and supplementary angles. Define and identify vertical angles and state their relationship. Define and identify adjacent angles and linear pairs. Apply the properties of complementary and supplementary angles to find unknown angle measures. Apply the properties of vertical angles and linear pairs to find unknown angle measures. Solve algebraic problems involving these angle relationships to find unknown values and angle measures. Ever wonder how architects ensure buildings stand straight or how pool players aim their shots? 📐 It's all about understanding angles! In this lesson, you'll learn about special angle pairs like complementary, supplementary, vertical, and adjacent angles. Mastering these relationships...

TermDefinitionExample AngleA figure formed by two rays sharing a common endpoint, called the vertex.The corner of a square is an angle, typically 90 degrees. VertexThe common endpoint of the two rays that form an angle.In angle ABC, point B is the vertex. Adjacent AnglesTwo angles that share a common vertex and a common side, but have no common interior points.If you cut a slice of pizza, the angle of your slice and the angle of the remaining pizza next to it are adjacent. Complementary AnglesTwo angles whose measures add up to exactly 90 degrees.An angle of 30 degrees and an angle of 60 degrees are complementary because 30 + 60 = 90. Supplementary AnglesTwo angles whose measures add up to exactly 180 degrees.An angle of 100 degrees and an angle of 80 degrees are supplementary because 100...

Complementary Angles Rule If $\angle A$ and $\angle B$ are complementary angles, then $m\angle A + m\angle B = 90^\circ$. Use this rule when two angles combine to form a right angle or are stated as complementary. Supplementary Angles Rule If $\angle C$ and $\angle D$ are supplementary angles, then $m\angle C + m\angle D = 180^\circ$. Apply this rule when two angles combine to form a straight line or are stated as supplementary. Vertical Angles Theorem If $\angle E$ and $\angle F$ are vertical angles, then $m\angle E = m\angle F$. Use this rule when two straight lines intersect, and you need to find the measure of an angle opposite a known angle. Linear Pair Postulate If $\angle G$ and $\angle H$ form a linear pair, then $m\angle G + m\angle H = 180^\circ$. T...