Do Now 1.9.14 “Unusual Area” Javier is helping his uncle to tile a patio that has an irregular shape. He needs to calculate the approximate number of tiles he will need to cover the inside of the figure shown to the right. What are some strategies you could give Javier to assist with his estimate? NOTE: Each Square is equal to 1 square foot.

We will solve for an unknown angle using properties of angles. NAME:______________________________ 1.9.14 Review Lesson 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. 31 59 59 127.5 + 31 52.5 127.5 + 52.5 90 180 Right angle Straight angle Students, you already know the measure of a right angle (90) and a straight angle (180). 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 68 + 22 = 90 113 + 67 = 180 68 22 A Complementary Complementary Supplementary Corner Straight 67 113 B Supplementary 33 57 61 119 60 + 30 = 90 125 + 55 = 180 57 is the complement of 33. 119 is the supplement of 61. Go to Skill Dev 1 1 distinctive feature of Vocabulary

Can adjacent angles also be vertical? 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 vertical angles? How do you know? Explain why the other figure shows adjacent angles. CFU 2 A B 121.3 45 65 65 + 45 = 110 121 = 121 Vertical angles share only a vertex. The angle measures are equivalent. Go to Skill Dev 2 Can adjacent angles also be vertical?

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? Once I/you substitute the given angle measure(s) into the equation, how can I solve for the missing angle? CFU 1 2 1. What is the measure of angle x? 2. What is the measure of angle x? 3. What is the complement of a 38 angle? 4. What is the complement of an 13.5 angle? 32.5 x m∠x + 32.5 = 90.0 x 58 m∠x + 58 = 90 - 32.5 - 32.5 - 58 - 58 m∠x = 57.5 m∠x = 32 Property of Angle: ______________ Measure: _____________________ complementary Property of Angle: ______________ Measure: _____________________ complementary m∠x = 57.5 m∠x = 32 m∠x + 38 = 90 m∠x + 13.5 = 90.0 - 38 - 38 - 13.5 -13.5 2 figure out 3 replace Vocabulary m∠x = 52 m∠x = 76.5

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? Once I/you substitute the given angle measure(s) into the equation, how can I solve for the missing angle? CFU 1 2 5. What is the measure of ∠1? 6. What is the measure of ∠2? 7. What is the supplement of a 120.4 angle? 8. What is the supplement of a 30.5 angle? m∠1 + 106.7 = 180.0 m∠2 + 63.5 = 180.0 - 106.7 -106.7 - 63.5 - 63.5 1 106.7 63.5 2 m∠1 = 73.3 m∠2 = 116.5 Property of Angle: ______________ Measure: _____________________ supplementary Property of Angle: ______________ Measure: _____________________ supplementary m∠1 = 73.3 m∠2 = 116.5 m∠x + 120.4 = 180.0 m∠x + 30.5 = 180.0 - 120.4 - 120.4 - 30.5 - 30.5 m∠x = 59.6 m∠x = 149.5 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? Once I/you substitute the given angle measure(s) into the equation, how can I solve for the missing angle? CFU 1 2 9. What is the measure of angle x? 10. What is the measure of angle x? 71.5 35 x 127.3 42 x 71.5 + 35 = m∠x m∠x + 42 = 127.3 106.5 = m∠x - 42 - 42 m∠x = 85 Property of Angle: ______________ Measure: _____________________ adjacent Property of Angle: ______________ Measure: _____________________ adjacent m∠x = 106.5 m∠x = 85.3

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? Once I/you substitute the given angle measure(s) into the equation, how can I solve for the missing angle? CFU 1 2 11. What is the measure of angle x? 12. What is the measure of angle x? 75.7 x 88 x 88 = m∠x m∠x = 75.7 Property of Angle: ______________ Measure: _____________________ vertical Property of Angle: ______________ Measure: _____________________ vertical m∠x = 88 m∠x = 75.7

90° 47° 43° 90° Angle w is supplementary to the sum of angles x & y 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 Angle w is supplementary to the sum of angles x & y 90° 47° Angle x is supplementary to angle y Angle w is vertical to the 43° angle. 43° Angle z is vertical to angle w. It is also supplementary to x & y 90°

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. 43 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 43 angle, at what angle will the red car turn? m∠x = 47 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 25 angle? A 65 B 135 C 155 D 165 __

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 53.5 m∠x + 53.5 = 90.0 1 115 m∠1 + 115 = 180 - 53.5 - 53.5 - 115 - 115 m∠x = 36.5 m∠1 = 65 Word Bank angle complementary supplementary adjacent vertical unknown complementary supplementary m∠x = 36.5 m∠1 = 65 Access Common Core m∠A = 55 m∠B = 30 m∠C = 150 m∠D = 35 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 51.4 angle? 4. What is the supplement of a 62.6 angle? 27.3 1 x 128.5 m∠x + 128.5 = 180.0 m∠1 + 27.3 = 90.0 - 128.5 -128.5 - 27.3 -27.3 m∠x = 51.5 m∠1 = 62.7 Property of Angle: ______________ Measure: _____________________ complementary Property of Angle: ______________ Measure: _____________________ supplementary m∠1 = 62.7 m∠x = 51.5 m∠x + 51.4 = 90.0 m∠x + 62.6 = 180.0 - 51.4 - 51.4 - 62.6 - 62.6 m∠x = 38.6 m∠x = 117.4

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? 85.3 40 x 117 x 85.3 + 40 = m∠x 125.3 = m∠x m∠x = 117 Property of Angle: ______________ Measure: _____________________ adjacent Property of Angle: ______________ Measure: _____________________ vertical m∠x = 125.3 m∠x = 117

x y y 1. What is the measure of angle x? Independent Practice (Cont.) 1. What is the measure of angle x? y 34.3° x 75° 34.3° + m∠x = 90.0° – 34.3° – 34.3° m∠x = 55.7° 2. What is the measure of angle y? 34.3° = m∠y (They are Vertical Angles) 34.3° = 34.3° Access Common Core Felicia thinks that the measure of angle x is 16°. Explain the mistake she made. Felicia confused supplementary angles with complementary angles. The sum of x and 79° should be 180°, not 90°. x 79° Xavier thinks that the measure of angle y is 89.5°. Explain the mistake he made. 90.5° y Xavier confused vertical angles with supplementary angles. Angle y should be 90.5° because vertical angles are equal in measure.

Hint: X + X = 90 Hint: X + 2X = 180 m∠x + 37 = 90 m∠x + 51 = 90 Homework Hint: X + X = 90 m∠x + 37 = 90 m∠x + 51 = 90 m∠x + m∠x  = 90 - 37 - 37 - 51 - 51 2x = 90 m∠x = 53 m∠x = 39 m∠x = 45 Hint: X + 2X = 180 m∠x + 116 = 180 m∠x + 34 = 180 m∠x + m∠2x = 180 - 116 - 116 - 34 - 34 3x = 180 m∠x = 64 m∠x = 146 m∠x = 60

Homework Use your knowledge of vertical angles, supplementary angles, complementary angles, and adjacent angles to determine the unknown angles for each figure below. HINT: It may be necessary to solve for variables (not in alphabetical order) 31° Angle w is vertical to angle y. Angle x is supplementary to either angle w or angle y. 132° Angle x is vertical to the 132° angle. 149° Angle y is supplementary to the 132° angle. 31° Angle y is supplementary to the 59° angle. 48° 48° Angle z is vertical to angle y. It is also supplementary to the 132° angle. 90° Angle z is given as a 90° (right) angle.