Do Now 1.8.14 “Dot Talk”

We will solve for an unknown angle using properties of angles. Learning Objective We will solve for an unknown angle using properties of angles. 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. What are we going to do? CFU Activate Prior Knowledge A right angle is an angle that measures 90. A straight angle is an angle that measures 180. Add the angle measures. 1. 2. 30 60 60 125 + 30 55 125 + 55 90 180 Right angle Straight angle Students, you already know the measure of a right angle and a straight angle. Now, we will use these angles to help us solve for unknown angles. Make Connection

Complementary Angles Supplementary Concept Development 1 Properties1 of Angles Complementary Angles Supplementary m∠A + m∠B = 90° m∠A + m∠B = 180° Two angles are complementary angles if their sum is 90°. supplementary angles if their sum is 180°. 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 1 70 + 20 = 90 115 + 65 = 180 70 20 A Complementary Complementary Supplementary Corner Straight 65 115 B Supplementary 30 60 55 125 60 + 30 = 90 125 + 55 = 180 60 is the complement of 30. 125 is the supplement of 55. Go to Skill Dev 1 1 distinctive feature of Vocabulary

if they are formed by two intersecting lines and are not adjacent. Concept Development 2 Properties of Angles Adjacent Angles Vertical m∠A + m∠B = m∠C m∠A = m∠B Two angles are adjacent angles if they share a common ray and endpoint. vertical angles if they are formed by two intersecting lines and are not adjacent. Which of the following figures shows adjacent angles? How do you know? Explain why the other figure shows vertical angles. CFU 2 A B 125 40 70 70 + 40 = 110 125 = 125 Go to Skill Dev 2

Complementary Angles Supplementary Angles Skill Development/Guided Practice 1 Complementary Angles m∠A + m∠B = 90° Supplementary Angles m∠A + m∠B = 180° Determine2 the property of angles needed. Solve for the unknown angle measure using the property of angles as follows: Substitute3 the given angle measure(s) into the equation. Solve the equation. Write the solution using the angle measure and degree symbol (m∠x = 45). Solve for unknown angle measures using properties of angles. 1 2 3 a b How did I/you determine the property of angles needed? How did I/you substitute the given angle measure(s) into the equation? CFU 1 2a 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? 35 x m∠x + 35 = 90 x 50 m∠x + 50 = 90 - 35 - 35 - 50 - 50 m∠x = 55 m∠x = 40 Property of Angle: ______________ Measure: _____________________ complementary Property of Angle: ______________ Measure: _____________________ complementary m∠x = 55 m∠x = 40 m∠x + 19 = 90 m∠x + 85 = 90 - 19 - 19 - 85 - 85 2 figure out 3 replace Vocabulary m∠x = 71 m∠x = 5

Complementary Angles Supplementary Angles Skill Development/Guided Practice 1 (continued) Complementary Angles m∠A + m∠B = 90° Supplementary Angles m∠A + m∠B = 180° Determine the property of angles needed. Solve for the unknown angle measure using the property of angles as follows: Substitute the given angle measure(s) into the equation. Solve the equation. Write the solution using the angle measure and degree symbol (m∠x = 45). Solve for unknown angle measures using properties of angles. 1 2 3 a b How did I/you determine the property of angles needed? How did I/you substitute the given angle measure(s) into the equation? CFU 1 2a 5. What is the measure of ∠1? 6. What is the measure of ∠2? 7. What is the supplement of a 125 angle? 8. What is the supplement of a 30 angle? m∠1 + 110 = 180 m∠2 + 68 = 180 - 110 - 110 - 68 - 68 1 110 68 2 m∠1 = 70 m∠2 = 112 Property of Angle: ______________ Measure: _____________________ supplementary Property of Angle: ______________ Measure: _____________________ supplementary m∠1 = 70 m∠2 = 112 m∠x + 125 = 180 m∠x + 30 = 180 - 125 - 125 - 30 - 30 m∠x = 55 m∠x = 150 Go to Concept Dev 2

x x Adjacent Angles Vertical Angles Skill Development/Guided Practice 2 Adjacent Angles m∠A + m∠B = m∠C Vertical Angles m∠A = m∠B Determine the property of angles needed. Solve for the unknown angle measure using the property of angles as follows: Substitute the given angle measure(s) into the equation. Solve the equation. Write the solution using the angle measure and degree symbol (m∠x = 45). Solve for unknown angle measures using properties of angles. 1 2 3 a b How did I/you determine the property of angles needed? How did I/you substitute the given angle measure(s) into the equation? CFU 1 2a 9. What is the measure of angle x? 10. What is the measure of angle x? 75 35 x 127 42 x 75 + 35 = m∠x m∠x + 42 = 127 110 = m∠x - 42 - 42 m∠x = 85 Property of Angle: ______________ Measure: _____________________ adjacent Property of Angle: ______________ Measure: _____________________ adjacent m∠x = 110 m∠x = 85

x x Adjacent Angles Vertical Angles Skill Development/Guided Practice 2 (continued) Adjacent Angles m∠A + m∠B = m∠C Vertical Angles m∠A = m∠B Determine the property of angles needed. Solve for the unknown angle measure using the property of angles as follows: Substitute the given angle measure(s) into the equation. Solve the equation. Write the solution using the angle measure and degree symbol (m∠x = 45). Solve for unknown angle measures using properties of angles. 1 2 3 a b How did I/you determine the property of angles needed? How did I/you substitute the given angle measure(s) into the equation? CFU 1 2a 11. What is the measure of angle x? 12. What is the measure of angle x? 75 x 87 x 87 = m∠x m∠x = 75 Property of Angle: ______________ Measure: _____________________ vertical Property of Angle: ______________ Measure: _____________________ vertical m∠x = 87 m∠x = 75

x y z 13. What is the measure of angle x? Skill Development/Guided Practice 2 (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 2 1 3 4 5 61 y 23 x 26 z 23 26 38 13. What is the measure of angle x? 15. What is the measure of angle z? 23 + m∠x = 61 61 + 23 + m∠z = 180 – 23 – 23 84 + m∠z = 180 m∠x = 38 – 84 – 84 m∠z = 96 14. What is the measure of angle y? 26 + 38 = m∠y 64 = m∠y

Relevance Complementary Angles m∠A + m∠B = 90° Supplementary Angles m∠A + m∠B = 180° Adjacent Angles m∠A + m∠B = m∠C Vertical Angles m∠A = m∠B 1 Solving for unknown angle measures using properties of angles will help you solve real-world problems. 40 x Baker St. Main St. First St. Baker St. intersects Main St. and First St. forming two complementary angles. If the orange car turns at a 40 angle, at what angle will the red car turn? 2 Solving for an unknown angle using properties of angles will help you do well on tests. Does anyone else have another reason why it is relevant to solve for an unknown angle using properties of angles? (Pair-Share) Why is it relevant to solve for an unknown angle using properties of angles? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU Sample Test Question: 79. What is the supplement of a 40 angle? A 50 B 130 C 140 D 220

Complementary Angles m∠A + m∠B = 90° Supplementary Angles m∠A + m∠B = 180° Adjacent Angles m∠A + m∠B = m∠C Vertical Angles m∠A = m∠B Word Bank Skill Closure Determine the property of angles needed. Solve for the unknown angle measure using the property of angles as follows: Substitute the given angle measure(s) into the equation. Solve the equation. Write the solution using the angle measure and degree symbol (m∠x = 45). Solve for unknown angle measures using properties of angles. 1 2 3 a b 1. What is the measure of angle x? Property of Angle: __________________ Measure: _____________________ 2. What is the measure of ∠1? x 48 m∠x + 48 = 90 1 108 m∠1 + 108 = 180 - 48 - 48 - 108 - 108 m∠x = 42 m∠1 = 72 Word Bank angle complementary supplementary adjacent vertical unknown complementary supplementary m∠x = 42 m∠1 = 72 Access Common Core m∠A = 50 m∠B = 30 m∠C = 130 m∠D = 40 Which two angles would form complementary angles? How do you know? Which two angles would form supplementary angles? m∠A + m∠D = 90° m∠A + m∠C = 180° Summary Closure What did you learn today about solving for unknown angle measures using properties of angles? (Pair-Share) Use words from the word bank.

Determine the property of angles needed. Independent Practice Complementary Angles m∠A + m∠B = 90° Supplementary Angles m∠A + m∠B = 180° Adjacent Angles m∠A + m∠B = m∠C Vertical Angles m∠A = m∠B Determine the property of angles needed. Solve for the unknown angle measure using the property of angles as follows: Substitute the given angle measure(s) into the equation. Solve the equation. Write the solution using the angle measure and degree symbol (m∠x = 45). Solve for unknown angle measures using properties of angles. 1 2 3 a b 1. What is the measure of ∠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? 25 1 x 136 m∠x + 136 = 180 m∠1 + 25 = 90 - 136 - 136 - 25 - 25 m∠x = 44 m∠1 = 65 Property of Angle: ______________ Measure: _____________________ complementary Property of Angle: ______________ Measure: _____________________ supplementary m∠1 = 65 m∠x = 44 m∠x + 51 = 90 m∠x + 62 = 180 - 51 - 51 - 62 - 62 m∠x = 39 m∠x = 118

x x Complementary Angles Supplementary Angles Adjacent Angles Independent Practice (continued) Complementary Angles m∠A + m∠B = 90° Supplementary Angles m∠A + m∠B = 180° Adjacent Angles m∠A + m∠B = m∠C Vertical Angles m∠A = m∠B Determine the property of angles needed. Solve for the unknown angle measure using the property of angles as follows: Substitute the given angle measure(s) into the equation. Solve the equation. Write the solution using the angle measure and degree symbol (m∠x = 45). Solve for unknown angle measures using properties of angles. 1 2 3 a b 5. What is the measure of angle x? 6. What is the measure of angle x? 85 40 x 110 x 85 + 40 = m∠x 125 = m∠x m∠x = 110 Property of Angle: ______________ Measure: _____________________ adjacent Property of Angle: ______________ Measure: _____________________ vertical m∠x = 125 m∠x = 110

y x z 7. What is the measure of angle x? Independent Practice (continued) 51 y 38 x 63 z 7. What is the measure of angle x? 9. What is the measure of angle z? 63 + 51 + m∠x = 180 m∠z = 51 114 + m∠x = 180 – 114 – 114 m∠x = 66 8. What is the measure of angle y? 38 + m∠y = 66 – 38 – 38 m∠y = 28

y x a z 1. What is the measure of angle x? Periodic Review 1 1. What is the measure of angle x? 64° y 28° x 77° z 106° a 28° + m∠x = 64° – 28° – 28° m∠x = 36° 2. What is the measure of angle y? 64° + m∠y = 180° – 64° – 64° m∠y = 116° 3. What is the measure of angle z? 106° + m∠z = 180° – 106° – 106° m∠z = 74° Access Common Core Describe how you would find the measure of angle a in the figure above. (Answers may vary) Angle a is supplementary to the sum of 77° and 64° because it forms a straight angle with these two angles. To solve for a, subtract the sum of 77° and 64° from 180°.

x y y 1. What is the measure of angle x? Periodic Review 2 1. What is the measure of angle x? y 35° x 75° 35° + m∠x = 90° – 35° – 35° m∠x = 55° 2. What is the measure of angle y? 55° + 75° = m∠y 116° = m∠y Access Common Core Leonor thinks that the measure of angle x is 16°. Explain the mistake she made. Leonor confused supplementary angles with complementary angles. The sum of x and 74° should be 180°, not 90°. x 74° Matheus thinks that the measure of angle y is 87°. Explain the mistake he made. 93° y Matheus confused vertical angles with supplementary angles. Angle y should be 93° because vertical angles are equal in measure.

x y 1. What is the measure of angle x? Periodic Review 3 1. What is the measure of angle x? 29° + m∠x = 54° 54° y 29° x – 29° – 29° m∠x = 25° 2. What is the measure of angle y? 54° + m∠y = 180° – 54° – 54° m∠y = 126° Access Common Core Choose Yes or No to indicate which of the statements below are true. 51° y 38° x 63° z f The measure of angle x is equal to the measure of angle y plus 38°. The measure of angle f is 51°. The measure of angle x can be found using supplementary angles. The measure of angle z is 51°. O Yes O No