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Learning Objective Name ___________________________

Learning Objective Name ___________________________ Today, we will solve for unknown angle measures using properties of angles. * Pre-requisite: AF 1.1 Solving one-step equation. 55°. 30°. CFU What are we going to do today?. Activate (or provide) Prior Knowledge.

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Learning Objective Name ___________________________

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  1. Learning ObjectiveName ___________________________ Today, we will solve for unknown angle measures using properties of angles. * Pre-requisite: AF 1.1 Solving one-step equation 55° 30° CFU What are we going to do today? Activate (or provide) Prior Knowledge A right angle is an angle that measures 90º. A straight angleis 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° 125° 60° + 55° + 30° 125° 180° 90° Straight angle Right 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.

  2. Concept Development Complementary Angles Supplementary Angles B 70° 60° 50° A C 125° + 55° = 180° 60° + 30° = 90° 60° + 70° + 50° = 180° 30° Two angles are complementary angles if their sum is 90º. Two angles are supplementary angles if their sum is 180º. The sum of the three interior2 angles of a triangle is 180º. 55° Go To Skill Dev #2 Go To Skill Dev #1 B A Supplementary Complementary 70° 20° 115° 65° Properties1 of Angles 1 facts about something Interior Angles of a Triangle 2 inside Complementary Supplementary Straight Corner 60° 125° 60º is the complement of 30º. 125º is the supplement of 55º. 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. 70° + 20° = 90° 115° + 65° = 180° 40° + 30° + 100° ≠ 180°

  3. Skill Development/Guided Practice 1 Complementary Angles Supplementary Angles Interior Angles of a Triangle 35° Solve for unknown angle measures using properties of angles. Step #1: Determine2 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 ( ). 2 figure out 3 replace -50 -50 -35 -35 x x 50° complementary complementary Property of Angle: __________________ Measure: _____________________ Property of Angle: __________________ Measure: _____________________ -85 -85 -19 -19 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?

  4. Skill Development/Guided Practice 1 (continued) Complementary Angles Supplementary Angles Interior Angles of a Triangle Return to Concept 1 110° 68° 2 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 ( ). -68 -68 -110 -110 supplementary supplementary Property of Angle: __________________ Measure: _____________________ Property of Angle: __________________ Measure: _____________________ -30 -30 -125 -125 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?

  5. Complementary Angles Supplementary Angles Interior Angles of a Triangle 75° x 35° x 56° 94° Skill Development/Guided Practice 2 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 ( ). -150 -150 -110 -110 Property of Angle: __________________ Measure: _____________________ Property of Angle: __________________ Measure: _____________________ interior angles of a triangle interior angles of a triangle 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?

  6. Complementary Angles Supplementary Angles Interior Angles of a Triangle 60° 35° y y x z x 95° z Skill Development/Guided Practice 2 (continued) 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 ( ). + 35 + 95 = 180 + 60 + 90 = 180 + 130 = 180 + 150 = 180 –130 –130 –150 –150 = 30 = 50 + 50 = 90 + 30 = 180 + 95 = 180 + 150 = 180 –50 –50 –30 –30 –95 –95 –150 –150 = 40 = 150 = 85 = 30 Measures: _____________________ 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?

  7. Relevance Complementary Angles Supplementary Angles Interior Angles of a Triangle 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 2 = 3x + 30° = 3(15°)+30° = 45°+30° so, m 2= 75° Angle 1 = x so, m 1 =15° 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. 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?

  8. Complementary Angles Supplementary Angles Interior Angles of a Triangle x 1 108° 48° Skill Closure Solve for unknown angle measures using properties of angles. -48 -48 -108 -108 complementary supplementary 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? ______________________________________________________________________ ______________________________________________________________________ Summary Closure What did you learn today about solving for unknown angle measures using properties of angles? Day 1 ______________________________________________________________________ Day 2 ______________________________________________________________________

  9. Independent Practice Name ________________________________ Complementary Angles Supplementary Angles Interior Angles of a Triangle 25° 1 136° x 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 ( ). -25 -25 -136 -136 supplementary complementary Property of Angle: __________________ Measure: _____________________ Property of Angle: __________________ Measure: _____________________ -51 -51 -62 -62

  10. Independent Practice (continued) Complementary Angles Supplementary Angles Interior Angles of a Triangle 65° 35° 1 z 105° y 28° x 40° 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 ( ). -28 -28 -100 -100 -35 -35 -145 -145 Property of Angle: __________________ Measure: _____________________ interior angles of a triangle Measures: ________________________

  11. Periodic Review 1 Name ________________________________ Complementary Angles Supplementary Angles Interior Angles of a Triangle 52° 33° 2 1 23° x 1 69° 28° x y 72° 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 ( ). -23 -23 -69 -69 complementary supplementary -33 -33 -142 -142 -28 -28 -72 -72 -75 -75 -41 -41

  12. Periodic Review 2 Name ________________________________ Complementary Angles Supplementary Angles Interior Angles of a Triangle 48° y x z 22° 30° 40° x y 140° 48° 2 3 1 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 ( ). 38° -140 -140 -52 -52 -40 -40 -38 -38 1 52° 2 -42 -42 -72 -72 -138 -138 138˚ -138 -138 -48 -48 -22 -22 -1 -1 -1 -1

  13. Periodic Review 3 Name ________________________________ Complementary Angles Supplementary Angles Interior Angles of a Triangle 47° 53° y x 51° 37° x z y 154° 115° 1 55° 3 2 55° 65° 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 ( ). -71 -71 -53 -53 71° -47 -47 -67 -67 3 2 1 67° -115 -115 -37 -37 -154 -154 -120 -120 -115 -115 -141 -141 -76 -76 -34 -34

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