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.184.108.40.206 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.220.127.116.11x 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
- Page 8 Measuring Angles: Real-Life Objects - Page 9 Draw Angles - Page 10 Draw Angles: More Practice - Page 11 Put It All Together: Measure & Draw Angles - Page 12 Joining Angles - Page 13 Joining More Than Two Angles - Page 14 More Practice: Joining Angles - Page 15 Separating Angles .
Adjacent angles are two angles that share a common vertex and side, but have no common interior points. 5 and 6 are adjacent angles 7 and 8 are nonadjacent angles. Notes: Linear Pairs and Vertical Angles Two adjacent angles are a linear pair when Two angles are vertical angles when their noncommon sides are opposite rays.
two acute vertical angles 62/87,21 Vertical angles are two nonadjacent angles formed by two intersecting lines. You can use the corner of a piece of paper to see that Ø ZVY and Ø WVU are less than right angles. 7KHUHIRUH DQG DUHDFXWHYHUWLFDO angles. two obtuse adjacent angles 62/87,21 Adjacent angles are two angles that lie in the same
two acute vertical angles . Geometry Unit 2 Note Sheets (Segments, Lines & Angles) 6 Angle Pair Relationships Vertical Angles Complementary Angles Supplementary Angles Linear Pair Guided Practice 5. Find the measures of two supplementary angles if the measures of one angles is 6 less than five t
vertical angles. Vertical angles have the same measure. Vertical angles are also called opposite angles. 1 and 2 are vertical angles. 3 and 4 are vertical angles. 14. In this triangle, name a pair of complementary angles. m T 30 m L 60 30 60 90 . So T and L are complementary angles. 15. In this parallelogram, name a pair of .
Adjacent Angles: Two angles and with a common side ⃗⃗⃗⃗⃗ are adjacent angles if belongs to the interior of . Vertical Angles: Two angles are vertical angles (or vertically opposite angles) if their sides form two pairs of opposite rays. Angles on a Line: The sum of the me
Aug 18, 2015 · Measure and classify angles. Identify and use congruent angles and the bisector of an angle. Discover relationships between special pair of angles. Vocabulary Degree, ray, angle, sides, vertex, interior, exterior, right angle, acute angle, obtuse angle, angle bisector. Adjacent angles, linear pair angles, vertical ang
Agile software development with Scrum is first introduced with its elements. Next, we use three development process lenses (communication, coordination, and control) to study how Scrum supports each of development processes, how they are related each other, and how they affect the performance of Scrum. In the following section, we analyze Scrum practices from social factor theories (social .