5.1 Classifying Angles

English5.1SpanishClassifying AnglesHow can you classify two angles ascomplementary or supplementary?Classification of AnglesAcute:Right:Obtuse:Straight:Less than 90 Equal to 90 Greater than 90 andless than 180 Equal to 180 1ACTIVITY: Complementary and Supplementary AnglesWork with a partner. Copy and complete each table. Graph each function. Is the function linear? Write an equation for y as a function of x. Describe the domain of each function.a. Two angles are complementaryif the sum of their measures is90 . In the table, x and y arecomplementary.15 x30 45 60 y9080706050403020100 10 20 30 40 50 60 70 80 90 xAngle measure (degrees)Chapter 560 90 120 150 y018430 xAngle measure (degrees)Angle measure (degrees)y75 b. Two angles are supplementaryif the sum of their measures is180 . In the table, x and y aresupplementary.Angles and e measure (degrees)x

EnglishSpanish2ACTIVITY: Exploring Rules About AnglesWork with a partner. Copy and complete each sentence with always,sometimes, or never.a. If x and y are complementary angles, then both x and y areb. If x and y are supplementary angles, then x isc. If x is a right angle, then x is3acute.acute.acute.ACTIVITY: Naming AnglesSome angles, such as A, can be named by a single letter. When this does notclearly identify an angle, you should use three letters, as follows. BDEPoint on one sidePoint on other sideVertexBAC AABEF andBCDE aresquares. BDEFEDWork with a partner.a. Name all pairs of complementary angles in the diagram above.b. Name all pairs of supplementary angles in the diagram above.4. IN YOUR OWN WORDS How can you classify two angles ascomplementary or supplementary? Give examples of each type.5. Find examples of real-life objects that use complementary andsupplementary angles. Make a drawing of each object andapproximate the degree measure of each angle.Use what you learned about classifying angles to completeExercises 3– 5 on page 188.Section 5.1Classifying Angles185

English5.1SpanishLessonLesson TutorialsKey Vocabularycomplementaryangles, p. 186supplementaryangles, p. 186congruent angles,p. 187vertical angles, p. 187Complementary AnglesWordsTwo angles are complementary angles if the sum of theirmeasures is 90 . 1 and 2 arecomplementary angles.Examples260 30 1Supplementary AnglesWordsTwo angles are supplementary angles if the sum of theirmeasures is 180 .Examples135 EXAMPLE345 4 3 and 4 aresupplementary angles.Classifying Pairs of Angles1Tell whether the angles are complementary, supplementary, or neither.a.70 110 70 110 180 So, the angles are supplementary.41 49 90 b.49 41 c.128 62 So, the angles are complementary.128 62 190 So, the angles are neither complementarynor supplementary.Tell whether the angles are complementary, supplementary, or neither.Exercises 6 –111.2.26 64 186Chapter 5136 44 Angles and Similarity3.70 19

EnglishSpanishCongruent AnglesWordsReadingTwo angles are congruent if they have the same measure.ExamplesArcs are used toindicate congruentangles.60 120 60 120 Vertical AnglesWordsTwo angles are vertical angles if they are opposite anglesformed by the intersection of two lines. Vertical anglesare congruent. 1 and 3 are vertical angles.1Examples42 2 and 4 are vertical angles.3EXAMPLEFinding Angle Measures2Find the value of x.a.70 x The angles are vertical angles.Because vertical angles are congruent,the angles have the same measure.So, x is 70.b.The angles are complementary.So, the sum of their measures is 90 .x 50 9050 x x 40So, x is 40.Find the value of x.Exercises 12 –144.5.85 x 6.x 69 x Section 5.1Classifying Angles187

EnglishSpanishExercises5.1Help with Homework1. VOCABULARY Explain the difference between complementary angles andsupplementary angles.2. WRITING When two lines intersect, how many pairs of vertical angles areformed? Explain.6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Tell whether the statement is always, sometimes, or never true. Explain.3. If x and y are supplementary angles, then x is obtuse.4. If x and y are right angles, then x and y are supplementary angles.5. If x and y are complementary angles, then y is a right angle.Tell whether the angles are complementary, supplementary, or neither.16.7.8.31 59 122 42 68 48 9.10.115 11.65 156 45 24 55 Find the value of x.2 12.13.14.x 128 117 x x 35 15. ERROR ANALYSIS Describe and correctthe error in finding the value of x.16. TRIBUTARY A tributary joins a river atan angle. Find the value of x.x 188Chapter 5127 Angles and Similarity The value of x is 55because verticalangles arecomplementary.x 35

EnglishSpanishFind the value of x.17.18.19.7x 75 (x 20) 4x (2x 1) 2x 20. OPEN-ENDED Give an exampleof an angle that can be asupplementary angle but cannotbe a complementary angle. Explain.ABC21. VANISHING POINT The vanishing pointof the picture is represented by point B.DFa. Name two pairs ofcomplementary angles.Eb. Name three pairs ofsupplementary angles.22. INTERSECTION What are the measures of theother three angles formed by the intersection?751050 132107523. RATIO The measures of two complementaryangles have a ratio of 3 : 2. What is the measureof the larger angle?24. REASONING Two angles are vertical angles. What are their measures if theyare also complementary angles? supplementary angles?25.Write and solve a system ofequations to find the values of x and y.7x y 5x 2y Solve the equation. Check your solution. (Section1.1 1.1and Section1.2)SECTION1.2SECTION26. x 60 45 18027. x 58.5 92.2 18028. x x 110 180129. MULTIPLE CHOICE The graph of which equation has a slope of — and passes2through the point (6, 4)? (Section3.2)SECTION3.2A y x 3 1B y — x 7 21C y — x 1 2Section 5.1MSNA8PE 0501.indd 1891D y —x 3 2Classifying Angles1895/19/10 2:18:32 PM

Vertical Angles Words Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent. Examples 4 2 3 1 1 and 3 are vertical angles. 2 and 4 are vertical angles. EXAMPLE 2 Finding Angle Measures Find the value of x. a. 70 x The