1 / 16

Do Now 1.9.14 “Unusual Area”

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.

etoile
Download Presentation

Do Now 1.9.14 “Unusual Area”

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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.

  2. NAME:______________________________ 1.9.14 Review Lesson 52.5 31 Learning Objective What are we going to do? CFU 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. Activate Prior Knowledge A right angleis an angle that measures 90. A straight angleis an angle that measures 180. Add the angle measures. 1. 2. 59 127.5 Make Connection 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. 59 127.5 + 31 + 52.5 90 180 Right angle Straight angle

  3. Concept Development 1 + 55 = 180 125 + 30 60 = 90 61 B A Supplementary Complementary 68 22 113 67 Properties1 of Angles 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 ____________. Go to Skill Dev 1 68 + 22 = 90 + 67 113 = 180 Complementary Supplementary Corner Straight 57 119 33 1 distinctive feature of Vocabulary 57is the complementof 33. 119 is the supplementof 61.

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

  5. Skill Development/Guided Practice 1 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 Solve for unknown angle measures using properties of angles. 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). 1 2 2 a b 3 m∠x + 58= 90 m∠x + 32.5 = 90.0 -32.5 - 32.5 -58 -58 m∠x = 32 m∠x = 57.5 x x 32.5 58 complementary complementary Property of Angle: ______________ Measure: _____________________ Property of Angle: ______________ Measure: _____________________ m∠x = 32 m∠x = 57.5 2 figure out 3 replace Vocabulary m∠x + 38= 90 m∠x + 13.5 = 90.0 -38 -38 -13.5 -13.5 m∠x = 52 m∠x = 76.5

  6. Skill Development/Guided Practice 1 (continued) 1 106.7 63.5 2 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 Solve for unknown angle measures using properties of angles. 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). 1 2 2 a b Go to Concept Dev 2 3 m∠1 + 106.7= 180.0 m∠2 + 63.5= 180.0 -63.5 -63.5 -106.7 -106.7 m∠2 = 116.5 m∠1 = 73.3 supplementary supplementary Property of Angle: ______________ Measure: _____________________ Property of Angle: ______________ Measure: _____________________ 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

  7. Skill Development/Guided Practice 2 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 Solve for unknown angle measures using properties of angles. 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). 1 2 2 a b 3 127.3 x 71.5 x 35 42 71.5+ 35 = m∠x m∠x + 42 = 127.3 - 42 - 42 106.5= m∠x m∠x = 85 adjacent adjacent Property of Angle: ______________ Measure: _____________________ Property of Angle: ______________ Measure: _____________________ m∠x = 106.5 m∠x = 85.3

  8. Skill Development/Guided Practice 2 (continued) 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 Solve for unknown angle measures using properties of angles. 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). 1 2 2 a b 3 x 75.7 88 x 88= m∠x m∠x = 75.7 vertical vertical Property of Angle: ______________ Measure: _____________________ Property of Angle: ______________ Measure: _____________________ m∠x = 88 m∠x = 75.7

  9. 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 1 2 3 4 5 Angle w is supplementary to the sum of angles x & y 90° Angle x is supplementary to angle y 47° Angle w is vertical to the 43° angle. 43° Angle z is vertical to angle w. It is also supplementary to x & y 90°

  10. Relevance Solving for unknown angle measures using properties of angles will help you solve real-world problems. 1 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 whatanglewill the red carturn? x m∠x = 47 43 Sample Test Question: 79. What is the supplement of a 25angle? A 65 B 135 C 155 D 165 Solving for an unknown angle using properties of angles will help you do well on tests. 2 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 __

  11. x 1 115 53.5 Skill Closure Solve for unknown angle measures using properties of angles. 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). 1 2 a b 3 Word Bank Word Bank angle complementary supplementary adjacent vertical unknown m∠1 + 115= 180 m∠x + 53.5= 90.0 -115 -115 -53.5 -53.5 m∠1 = 65 m∠x = 36.5 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? How do you know? 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.

  12. Independent Practice x 128.5 Solve for unknown angle measures using properties of angles. 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). 1 2 a b 3 27.3 1 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 complementary supplementary Property of Angle: ______________ Measure: _____________________ Property of Angle: ______________ Measure: _____________________ m∠x = 51.5 m∠1 = 62.7 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

  13. Independent Practice (continued) Solve for unknown angle measures using properties of angles. 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). 1 2 a b 3 x 85.3 x 40 117 85.3+ 40 = m∠x 125.3= m∠x m∠x = 117 adjacent vertical Property of Angle: ______________ Measure: _____________________ Property of Angle: ______________ Measure: _____________________ m∠x = 125.3 m∠x = 117

  14. Independent Practice (Cont.) x 79° 1. What is the measure of angle x? 34.3° + m∠x = 90.0° – 34.3° – 34.3° x m∠x = 55.7° 75° 34.3° 2. What is the measure of angle y? 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°. y Xavier thinks that the measure of angle y is 89.5°. Explain the mistake he made. 90.5° Xavier confused vertical angles with supplementary angles. Angle y should be 90.5° because vertical angles are equal in measure.

  15. Homework Hint: X + X = 90 m∠x + m∠x= 90 m∠x + 37= 90 m∠x + 51= 90 2x = 90 -37 -37 -51 -51 m∠x = 45 m∠x = 53 m∠x = 39 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

  16. 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° 149° Angle x is vertical to the 132° angle. Angle y is supplementary to the 59° angle. Angle y is supplementary to the 132° angle. 31° 48° Angle z is given as a 90° (right) angle. 48° Angle z is vertical to angle y. It is also supplementary to the 132° angle. 90°

More Related