1. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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. Learning Objective Name ___________________________ 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 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. Calculate the sum of the two smaller angles to check whether the whole angle is correctly labeled. Right angle AB Straight angle 60° + 30° 90° 125° + 55° 180° A right angle is an angle that measures 90º. A straight angle is an angle that measures 180º. 30° 60° 55° 125°

2. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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 CFU #1 How do you know that figure A shows complementary angles? Figure A shows complementary angles because ______________. How do you know that figure B shows supplementary angles? Figure B shows supplementary angles because ______________. CFU #2 The following three angles cannot form a triangle: 40°, 30°, and 100°. Explain why. 65° 115° B Supplementary 70° 20° A Complementary 70°+ 20°= 90° 115°+ 65°= 180° 40°+ 30°≠ 180°+ 100° C omplementary C orner 60°+ 30°= 90° Complementary Angles 30° 60° Two angles are complementary angles if their sum is 90º. S upplementary S traight 55° 125° + 55°= 180° Supplementary Angles Two angles are supplementary angles if their sum is 180º. Interior Angles of a Triangle A B C 60°50° 70° 60°+ 70°+ 50°= 180° The sum of the three interior 2 angles of a triangle is 180º. 2 inside Go To Skill Dev #1 Go To Skill Dev #2 Properties 1 of Angles 1 facts about something 60º is the complement of 30º.125º is the supplement of 55º.

3. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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. 1. What is the measure of angle x?2. What is the measure of angle x? 3. What is the complement of a 19° angle?4. What is the complement of an 85° angle? 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? x 50° 35° complementary Step #1: Determine 2 the property of angles needed. Step #2: Solve for the unknown angle measure using the property of angles as follows: a. Substitute 3 the given angle measure(s) into the equation. b. Solve the equation. Step #3: Write the solution using the angle measure and degree symbol ( ). 2 figure out 3 replace x -35 -50 complementary -19 -85 Property of Angle: __________________ Measure: _____________________ Property of Angle: __________________ Measure: _____________________ Interior Angles of a Triangle Supplementary Angles Complementary Angles Skill Development/Guided Practice 1 Solve for unknown angle measures using properties of angles.

4. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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) 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? 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 ( ). 5. What is the measure of angle 1?6. What is the measure of angle 2? 7. What is the supplement of a 125° angle?8. What is the supplement of a 30° angle? Property of Angle: __________________ Measure: _____________________ Property of Angle: __________________ Measure: _____________________ 1 110° 68° 2 -110 supplementary -68 supplementary -125 -30 Solve for unknown angle measures using properties of angles. Interior Angles of a Triangle Supplementary Angles Complementary Angles Return to Concept

5. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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. 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? Skill Development/Guided Practice 2 9. What is the measure of angle x?10. What is the measure of angle x? 75° 35° x 56° 94° x Property of Angle: __________________ Measure: _____________________ Property of Angle: __________________ Measure: _____________________ -110 interior angles of a triangle -150 interior angles of a triangle 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 ( ). Solve for unknown angle measures using properties of angles. Interior Angles of a Triangle Supplementary Angles Complementary Angles

6. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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. 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? Skill Development/Guided Practice 2 (continued) 11. What are the measures of angles x, y, and z?12. What are the measures of angles x, y, and z? Measures: _____________________ y z 95° 35° x x y 60° z + 35 + 95 = 180 + 130 = 180 –130 = 50 + 50 = 90 –50 = 40 + 95 = 180 –95 = 85 + 60 + 90 = 180 + 150 = 180 –150 = 30 + 30 = 180 –30 = 150 + 150 = 180 –150 = 30 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 ( ). Solve for unknown angle measures using properties of angles. Interior Angles of a Triangle Supplementary Angles Complementary Angles

7. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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 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? 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. Angle 1 = x so, m 1 = 15° Angle 2 = 3x + 30° = 3(15°)+30° = 45°+30° so, m 2= 75° 2. Solving for unknown angle measures using properties of angles will help you do well on tests. 1. Solving for unknown angle measures using properties of angles will prepare you to solve more difficult geometry problems. Interior Angles of a Triangle Supplementary Angles Complementary Angles

8. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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 Closure What did you learn today about solving for unknown angle measures using properties of angles? Day 1 ______________________________________________________________________ Day 2 ______________________________________________________________________ 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 ( ). Solve for unknown angle measures using properties of angles. Summary Closure 1. What is the measure of angle x? Property of Angle: __________________ Measure: _____________________ 2. What is the measure of angle 1? Property of Angle: __________________ Measure: _____________________ x 48° 1 108° -48 complementary -108 supplementary Interior Angles of a Triangle Supplementary Angles Complementary Angles Constructed Response 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?

9. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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. 1. What is the measure of angle 1?2. What is the measure of angle x? 3. What is the complement of a 51° angle?4. What is the supplement of a 62° angle? Independent Practice Name ________________________________ 25° 1 x 136° -25 -136 -62 -51 Property of Angle: __________________ Measure: _____________________ Property of Angle: __________________ Measure: _____________________ complementary supplementary 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 ( ). Solve for unknown angle measures using properties of angles. Interior Angles of a Triangle Supplementary Angles Complementary Angles

10. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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. 5. What is the measure of angle 1?6. What are the measures of angles x, y, and z? Independent Practice (continued) z 40 ° y 28 ° x 105 ° -28 -145 -35 65° 35° 1 Property of Angle: __________________ Measure: _____________________ -100 interior angles of a triangle Measures: ________________________ 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 ( ). Solve for unknown angle measures using properties of angles. Interior Angles of a Triangle Supplementary Angles Complementary Angles

11. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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. 1. What is the measure of angle x? Property of Angle: __________________ Measure: _____________________ 2. What is the measure of angle 1? Property of Angle: __________________ Measure: _____________________ 3. What are the measures of angles x and y? Measures: _____________________ 4. What are the measures of angles 1 and 2? Measures: _____________________ 5. What is the supplement of a 75° angle?6. What is the complement of a 41° angle? Periodic Review 1 Name ________________________________ 23° x 1 69° 2 52° 1 33° x y 72° 28° -23 complementary -69 supplementary -28 -72 -142 -33 -75 -41 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 ( ). Solve for unknown angle measures using properties of angles. Interior Angles of a Triangle Supplementary Angles Complementary Angles

12. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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. 1. What are the measures of angles 1 and 2? Measures: _____________________ 2. What are the measures angles of x and y? Measures: _____________________ 3. What are the measures of angles 1, 2, and 3? Measures: ________________________ 4. What are the measures of angles x, y, and z? Measures: _________________________ 5. What is the supplement of a 1° angle?6. What is the complement of a 1° angle? Periodic Review 2 Name ________________________________ y x 22 ° 30° 48 ° z 2 52° 1 38 ° x 40 ° y 140 ° 1 2 48 ° 3 -38 -38 -52 -40 -40 -140 -48 -48 -138 -138 -42 -42 -22 -138 -72 138˚ 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 ( ). Solve for unknown angle measures using properties of angles. Interior Angles of a Triangle Supplementary Angles Complementary Angles

13. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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. 1. What are the measures of angles x and y? Measures: _____________________ 2. What are the measures of angles 1, 2, and 3? Measures: _________________________ 3. What are the measures of angles x, y, and z? Measures: _____________________ 4. What are the measures of angles 1, 2, and 3? Measures: ____________________ 5. What is the supplement of a 34° angle?6. What is the complement of a 76° angle? Periodic Review 3 Name ________________________________ 3 71 ° 2 67 ° 1 y x 47 ° 53 ° 154° y 37° z x 51° 3 2 1 115 ° 55 ° 65 ° 55 ° -47 -47 -53 -67 -67 -71 -141 -154 -37 -115 -115 -120 -120 -115 -115 -34 -76 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 ( ). Solve for unknown angle measures using properties of angles. Interior Angles of a Triangle Supplementary Angles Complementary Angles

14. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th 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