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Name ___________________________ Learning Objective Today, we will solve for unknown angle measures using properties of angles. * Pre-requisite: AF 1.1 Solving one-step equation CFU What are we going to do today? Activate (or provide) Prior Knowledge A right angle is an angle that measures 90º. A straight angle is an angle that measures 180º. Calculate the sum of the two smaller angles to check whether the whole angle is correctly labeled. A B 60° 30° Right angle 60° + 30° 90° 125° 55° 125° + 55° 180° Straight angle CFU Students, you already know the measure of a right angle and a straight angle. Today, we will use these angles to help us solve for unknown angles. DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Concept Development Properties1 of Angles 1 facts about something Complementary Angles Supplementary Angles mA + mB = 90o mA + mB =180o Two angles are complementary angles if their sum is 90º. Two angles are supplementary angles if their sum is 180º. Interior Angles of a Triangle mA + mB + mC =180o The sum of the three interior2 angles of a triangle is 180º. 2 Complementary Corner 60° B Supplementary Straight 125° 30° 60°+ 30° = 90° 70° 55° 60° 125°+ 55° = 180° 60º is the complement of 30º. inside 50° A C 60°+ 70°+ 50° = 180° 125º is the supplement of 55º. CFU #1 How do you know that figure A shows complementary angles? Figure A shows complementary angles because ______________. 70° + 20° = 90° How do you know that figure B shows supplementary angles? 115°+ 65° = 180° Figure B shows supplementary angles because ______________. Go To Skill Dev #1 A Go To Skill Dev #2 B 70° 20° Complementary 115° 65° Supplementary CFU #2 The following three angles cannot form a triangle: 40°, 30°, and 100°. Explain why. DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 40° + 30° + 100° ≠ 180° 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Skill Development/Guided Practice 1 Solve for unknown angle measures using properties of angles. Complementary Angles Supplementary Angles Interior Angles of a Triangle mA + mB = 90o mA + mB = 180o mA + mB + mC = 180o Determine2 Step #1: the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute3 the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 2 3 figure out replace 1. What is the measure of angle x? 2. What is the measure of angle x? mx + 35 = 90 -35 -35 x mx = 55 35° complementary Property of Angle: __________________ Measure: _____________________ mx 55 3. What is the complement of a 19° angle? mx +19 = 90 -19 -19 mx = 71 mx + 50 = 90 -50 -50 mx = 40 x 50° complementary Property of Angle: __________________ Measure: _____________________ mx 40 4. What is the complement of an 85° angle? mx + 85 = 90 -85 -85 mx = 5 CFU (#1a) How did I/you determine the property of angles needed? (#2a) How did I/you substitute the given angle measure(s) into the equation? DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Skill Development/Guided Practice 1 (continued) Solve for unknown angle measures using properties of angles. Complementary Angles Supplementary Angles Interior Angles of a Triangle mA + mB = 90o mA + mB = 180o mA + mB + mC = 180o Step #1: Determine the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 5. What is the measure of angle 1? 110° 1 6. What is the measure of angle 2? m1 + 110 = 180 -110 -110 supplementary Property of Angle: __________________ Measure: _____________________ m1 70 7. What is the supplement of a 125° angle? m1 = 70 2 supplementary Property of Angle: __________________ Measure: _____________________ m1 112 8. What is the supplement of a 30° angle? mx + 30 = 180 -30 -30 mx = 150 -125 -125 mx = 55 CFU (#1a) How did I/you determine the property of angles needed? (#2a) How did I/you substitute the given angle measure(s) into the equation? (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] m2 = 112 68° mx +125 = 180 DataWORKS Educational Research m2 + 68 = 180 -68 -68 Return to Concept 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Skill Development/Guided Practice 2 Complementary Angles Supplementary Angles Interior Angles of a Triangle mA + mB = 90o mA + mB = 180o mA + mB + mC = 180o Solve for unknown angle measures using properties of angles. Step #1: Determine the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 9. What is the measure of angle x? x 75° x 10. What is the measure of angle x? 56° 94° 35° mx + 75 + 35 = 180 mx + 94 + 56 = 180 mx + 110 = 180 -110 -110 mx + 150 = 180 -150 -150 mx = 30 mx = 70 angles of a triangle Property of Angle:interior __________________ mx 30 Measure: _____________________ interior angles of a triangle Property of Angle: __________________ mx 70 Measure: _____________________ CFU (#1a) How did I/you determine the property of angles needed? (#2a) How did I/you substitute the given angle measure(s) into the equation? DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Skill Development/Guided Practice 2 (continued) Solve for unknown angle measures using properties of angles. Complementary Angles Supplementary Angles Interior Angles of a Triangle mA + mB = 90o mA + mB = 180o mA + mB + mC = 180o Step #1: Determine the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 11. What are the measures of angles x, y, and z? 12. What are the measures of angles x, y, and z? mx + 35 + 95 = 180 mx + 130 = 180 35° y x 95° z –130 –130 mx = 50 mx + 150 = 180 x –150 –150 mx = 30 y z my + 50 = 90 mz + 95 = 180 –50 –50 –95 –95 mz = 85 my = 40 mx + 60 + 90 = 180 60° my + 30 = 180 –30 my mx 50 my 40 mz + 150 = 180 –30 = 150 –150 –150 mz = 30 mx 30 my 150 mz 30 Measures: _____________________ mz 85 Measures: _____________________ CFU (#1a) How did I/you determine the property of angles needed? (#2a) How did I/you substitute the given angle measure(s) into the equation? DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Relevance Complementary Angles Supplementary Angles Interior Angles of a Triangle mA + mB = 90o mA + mB = 180o mA + mB + mC = 180o 1. Solving for unknown angle measures using properties of angles will prepare you to solve more difficult geometry problems. 2. Solving for unknown angle measures using properties of angles will help you do well on tests. Angle 1 and Angle 2 are complementary. Angle 1 has a value of x; Angle 2 has a value of 3x + 30°. Find the measure of Angle 1 and Angle 2. 1 2 ( x ) (3 x 30) 90 4 x 30 90 4 x 60 x 15 Angle 1 = x so, m 1 = 15° Angle 2 = 3x + 30° = 3(15°)+30° = 45°+30° so, m 2= 75° CFU Does anyone else have another reason why it is relevant to solve for unknown angle measures using properties of angles? (pair-share) Why is it relevant to solve for unknown angle measures using properties of angles? You may give me one of my reasons or one of your own. Which reason is more relevant to you? Why? DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Complementary Angles Supplementary Angles Interior Angles of a Triangle mA + mB = 90o mA + mB = 180o mA + mB + mC = 180o Skill Closure Solve for unknown angle measures using properties of angles. Step #1: Determine the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 1. What is the measure of angle x? mx x 48° 2. What is the measure of angle 1? m1 +108 = 180 + 48 = 90 -48 -48 mx = 42 Property of Angle: complementary __________________ mx 42 Measure: _____________________ -108 108° 1 -108 m1 = 72 supplementary Property of Angle: __________________ Measure: _____________________ m1 72 Constructed Response Closure m A 50 m B 30 m C 130 m D 40 Summary Closure Which two angles to the left would form complementary angles? How do you know? Which two angles would form supplementary angles? How do you know? ______________________________________________________________________ ______________________________________________________________________ What did you learn today about solving for unknown angle measures using properties of angles? Day 1 ______________________________________________________________________ Day 2 ______________________________________________________________________ DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Name ________________________________ Independent Practice Complementary Angles Solve for unknown angle measures using properties of angles. mA + mB = 90o Supplementary Angles Interior Angles of a Triangle mA + mB = 180o mA + mB + mC = 180o Step #1: Determine the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 1. What is the measure of angle 1? 1 2. What is the measure of angle x? 25° 136° x m1 + 25 = 90 mx +136 = 180 -25 -25 -136 m1 = 65 mx complementary Property of Angle: __________________ m1 65 Measure: _____________________ 3. What is the complement of a 51° angle? -136 = 44 supplementary Property of Angle: __________________ Measure: _____________________ mx 44 4. What is the supplement of a 62° angle? mx + 51= 90 mx + 62 = 180 -51 -51 mx = 39 -62 -62 mx = 118 DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Independent Practice (continued) Complementary Angles Solve for unknown angle measures using properties of angles. mA + mB = 90o Supplementary Angles Interior Angles of a Triangle mA + mB = 180o mA + mB + mC = 180o Step #1: Determine the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 5. What is the measure of angle 1? 6. What are the measures of angles x, y, and z? 105° 40° z 35 y 28° x mx + 28 = 90 -28 -28 mx = 62 m1 + 65 + 35 = 180 m1 +100 = 180 -100 -100 m1 = 80 Property of Angle: interior __________________ angles of a triangle m 1 80 Measure: _____________________ DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] my + 40 105 = 180 my + 145 = 180 mz + 35 = 180 -145 -145 my = 35 mz = 145 -35 -35 mx my 62 35 mz 145 Measures: ________________________ 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Name ________________________________ Periodic Review 1 Complementary Angles Solve for unknown angle measures using properties of angles. mA + mB = 90o Supplementary Angles Interior Angles of a Triangle mA + mB = 180o mA + mB + mC = 180o Step #1: Determine the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 1. What is the measure of angle x? mx 23° x + 23 = 90 -23 -23 m x = 67 2. What is the measure of angle 1? 1 69° complementary Property of Angle: __________________ mx 67 Measure: _____________________ 3. What are the measures of angles x and y? 28° mx + 28 = 180 -28 -28 mx = 152 x 72° my + 72 = 90 -72 -72 my = 18 y 5. What is the supplement of a 75° angle? mx + 75 = 180 mx = 105 -75 -75 DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] -69 -69 m1 = 111 supplementary Property of Angle: __________________ m1 111 Measure: _____________________ 4. What are the measures of angles 1 and 2? m1 + 52 90 = 180 m1 + 142 = 180 -142 -142 52° m1 = 38 33° 2 mx 152 my 18 Measures: _____________________ m1 + 69 = 180 m2 + 33 = 90 -33 -33 m2 = 57 1 m1 38 m2 57 Measures: _____________________ 6. What is the complement of a 41° angle? mx + 41= 90 mx = 49 -41 -41 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Name ________________________________ Periodic Review 2 Complementary Angles Solve for unknown angle measures using properties of angles. mA + mB = 90o Supplementary Angles Interior Angles of a Triangle mA + mB = 180o mA + mB + mC = 180o Step #1: Determine the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 1. What are the measures of angles 1 and 2? 38° m1 + 38 = 90 1 -38 -38 m2 + 52 = 90 -52 -52 m2 = 38 m1 = 52 52° 2. What are the measures angles of x and y? mx + 40 = 180 my + 140 = 180 -140 -140 -40 -40 40° x my = 40 y 140° mx = 140 2 mx 140 my 40 Measures: _____________________ m1 52 m2 38 Measures: _____________________ 3. What are the measures of angles 1, 2, and 3? 48° 2 1 3 m3 + 42 = 180 -42 m2 + 48 + 90 = 180 m1 + 48 = 90 -48 -48 m1 = 42 m2 + 138 = 180 -138 -138 m2 = 42 -42 m3 = 138 30° m1 42 m2 42 m3 138 Measures: ________________________ 5. What is the supplement of a 1° angle? mx +1= 180 mx = 179 -1 -1 DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 4. What are the measures of angles x, y, and z? mz + 30 42 = 180 48° my + 138 = 180 mz + 72 = 180 42y -72 -72 -138 -138 x 138˚ z 22° my = 42 mz = 108 mx + 22 = 90 -22 -22 mx = 68 68 42 mz 108 Measures: _________________________ mx my 6. What is the complement of a 1° angle? mx +1= 90 mx = 89 -1 -1 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Name ________________________________ Periodic Review 3 Complementary Angles Solve for unknown angle measures using properties of angles. mA + mB = 90o Supplementary Angles Interior Angles of a Triangle mA + mB = 180o mA + mB + mC = 180o Step #1: Determine the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( mx 45). 1. What are the measures of angles x and y? mx + 47 = 90 47° my + 53 = 90 -53 -53 -47 -47 mx = 43 53° x 2. What are the measures of angles 1, 2, and 3? my = 37 m2 + 67 = 90 71° 3 2 y 67° -67 -67 1 z 154° mx + 51 90 = 180 mx +141= 180 -141 -141 mx = 39 -154 -154 my = 26 x y -37 -37 mz = 53 115° 1 3 2 55° 65° mx 39 my 26 mz 53 Measures: _____________________ 5. What is the supplement of a 34° angle? mx + 34 = 180 mx = 146 -34 -34 DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] m3 = 19 4. What are the measures of angles 1, 2, and 3? my + 154 = 180 mz + 37 = 90 37° 51° m2 = 23 -71 -71 m1 90 m2 23 Measures: _________________________ m3 19 mx 43 my 37 Measures: _____________________ 3. What are the measures of angles x, y, and z? m3 + 71 = 90 55° m1 + 115 = 180 -115 -115 m1 = 65 m2 + 65 + 55 = 180 m3 + 115 = 180 m2 + 120 = 180 -120 -120 m2 = 60 -115 -115 m3 = 65 m1 65 m2 60 m3 65 Measures: ____________________ 6. What is the complement of a 76° angle? mx + 76 = 90 mx = 14 -76 -76 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only. Blank Page DataWORKS Educational Research (800) 495-1550 • www.dataworks-ed.com ©2012 All rights reserved. Comments? [email protected] 6th Grade Measurement and Geometry 2.2 (4Q) Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Lesson to be used by EDI-trained teachers only.