This pdf includes the following topics:- Recognize complementary and supplementary angles Supplementary angles Application of Complementary and Supplementary Angles Adjacent Angles Linear Pair
1. 2.2 Complementary and Supplementary Angles Objective: Recognize complementary and supplementary angles Complementary angles are: two angles whose sum is 90 degrees (a right angle) each of the angles is called the complement of the other. Example 1: If an angle measures 38 degrees, what is its complement? 90 – 38 = x x = 52 x⁰ 38⁰ An illustration indicating the complement to an angle whose measure is also unknown (x): If the Then the complement angle = x x⁰ to angle x = (90 – x)⁰ The algebraic expression used to represent a complementary angle is 90 - x Remember! Complements Right Angle Sum 90
2. Definition Supplementary angles are: two angles whose sum is 180 degrees (a straight angle) each of the two angles is called the supplement of the other Example 2: If an angle measures 38 degrees, what is the measure of its supplement? 180 – 38 = x x = 142 x⁰ 38⁰ An illustration indicating the supplement of an angle whose unknown measure = x: If the Then the supplement angle = x to angle x = x⁰ (180 – x)⁰ The algebraic expression used to represent a supplementary angle is: 180 – x Remember! Supplements Straight Angle Sum 180 To keep from confusing the two, the following logic may help you remember: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 180 90 135 C comes before S in the alphabet, like 90 comes before 180 on a number line!
3. Application of Complementary and Supplementary Angles Example 3: Problem Solving: If the supplement of an angle is 4 times the measure of its complement, what is the measure of the angle? Name Expression Measure The Angle x Step 1: Make a table and a diagram! Complement 90 – x Supplement 180 - x 90 - x 180 - x x Step 2: Use the expressions in the table above to help you translate the problem into an the supplement of an angle is 4 times the measure of its complement 180 - x = 4( 90 – x) Step 3: Now we have this equation from our second table: 180 – x = 4(90 – x) solve algebraically 180 – x = 4(90 – x) 180 – x = 360 – 4x (distributed the 4) 3x = 180 (added 4x to each side, and subtracted 180 from each side) x = 60 (divided both sides by 3) This solution means “the angle” has a measure of 60 degrees. Step 4: Fill in the last column of table and answer the question! Sometimes you are asked for the measure of the complement or supplement, so make sure you re-read the question after finding all three measures! What is the measure of the angle? 60! Name Expression Measure The Angle x 60 Complement 90 – x 30 Supplement 180 - x 120
4. Other definitions useful for this section: Opposite Rays- Two rays with the same endpoint that extend in opposite directions and make up a straight line. A C A B A A B C A Adjacent Angles – Two angles that share a common vertex and a side but do not have any interior points in common. ∡BAD and ∡CAD ∡BAC and ∡CAD are NOT adjacent share vertex A and side AD with because their interiors overlap! no common interior points . . . So they ARE adjacent angles Linear Pair – A linear pair of angles are two adjacent angles whose outside rays form a straight angle (line). ∡BAD and ∡CAD are a linear pair! Psssst… Side Bar! By the way, you know or have figured out what adjacent means, right? If not … it means: “next to” or as the problems state it; “sharing a side.” Now look at the illustrations again with that in mind!
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