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Name Class Date Angle Relationships ni.; + i lit ii il.l i'lil,i: itiil i' Essential question: How can you use angle pairs to solue problems? PTORE Measuring and Describing Angles B \Mhen lines intersect, several angles are formed. Use a ruler or straightedge to draw a pair of intersecting lines. Label each angle in order clockwise from Use a protractor to find each angle measure. Angle I to 4. Angle Measure 1 2 3 4 c \.4rhat can you say about mll and ml3? Angles 1 and 3 are vertical angles. They are opposite one another. Vertical angles have equal measures, no sides in common, and no common interior points. \.44rat is D the other pair of vertical angles \Mhat can you say about ml| in A ? andml2? About ml2 andml3? c o o E Angles I and2 and angles 2 and 3 are adjacent angles. They share a common vertex and a common side. IJ o s .9 3 L= .= \Mhat are the two other pairs of adjacent angles in the figure? E f, i -o .g 5 \&hat can you say about the sum of the degree measures of each pair of c c o) adjacent angles? 5 - ()) Two angles whose measures add up to lB0o are called supplementary angles. Each pair of adjacent angles in the figure you made are angles. Two angles whose measures add up to g0o are called complemerrtary angles. REFTECT i 1, Angles AandBaresupplementary. Chapter 5 mlA: 775 B0".mlB = Lesson 1 EXAM P tE FindingAngle Measures Find the measure of IEHF, IEHF and angles. are The sum of their measures is :180 + Write and solve -- an equation to find mlEHF. 2x= nIEHF = TRY THIS! 2. Write and solve an equation to find the value of 3x and mlJML. nIJML:3x = e use the figure. 5Q 1. 2. 3, I fru. Name a pair of vertical angles. Name a pair of adjacent angles. @ Name a pair of supplementary angles. I ro t f 4. Name a pair of complementary angles. + _= f I D 5. Angle SUTmeasures 90". lVhat is rnlQUM 5. Angle RUNmeasures 51'. \Mhat is wISUR? c f, c q T f' @ 7. 8. n Two streets intersect. One of the angles formed measures 136'. The angles adjacent to the 136. angle each measure 2f . \.Alhat does x equal? \.4lhat is the degree measure of each of these adjacent angles? 3 o f Error Analysis Iames claims that when two adjacent angles measure 90' together, the two angles are supplementary. Explain why Iames is wrong. Chapter 5 176 Lesson 1 Date Additional Practice Use the diagram to name each figure. 1. a right angle 2. two acute angles 3. two obtuse angles 4. a pair of complementary angles 5. three pairs of supplementary angles c o Use the diagram to find each angle measure. E \ \n &-.d --a\J .= g .9 ...'E | 4\ e'\-" f L f o I 6. lf ml2: 1 10o. find ml4. 7. lf m11 = no, find mZ3. .= F =c 8. The diagram shows the intersection of three l I (9 roadways on a map. Based on the diagram, what should be the measure of IECD? Chapter 5 177 Practice and Problem Solving Frohlerm $olwin Use the flag of the Bahamas to solve the problems. 1. Name a right angle in the flag. G 2. Name a pair of comPlementarY tl ,--.1 angles in the flag. f 3. Name two acute angles in the flag. 4. Name a pair of suPPlementary angles in the flag. The diagram illustrates a ray of light being reflected off a mirror. The angle of incidence is congruent to the angle of reflection. Choose the letter for the best answer' 5. Name a pair of supplementary angles. A B C D ICMA, IAMN, INMB, I.AMB 1"NMC, IDMN IAMN, INAID 4A^t^ lljrs ^+ {-r} ln*id*nc* angles. F ZNMB, IBMD G IAMN, INMB J f rn!rr*r = I-AMD c f, tr g B. Find the measure of 14. F 650 G 350 ct3 D none 650 c 350 D 900 5 tr o H J 6' 250 900 10. Find the measure of 13. 9. Find the measure of 11. Chapter -o I 7. Which angle is congruentto 12? A B o f = ICMA, IDMB At1 Bt4 x 3 6. Name a pair of comPlementarY H ICMA, :rnnio nf refl*nti*n cli F 900 G 450 250 178 H J 350 650 Practice and Problem Solving f l @ ^o3 o l