Ms. Campos 7 th Grade. Unit 14- Angles
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1 Ms. Campos 7 th Grade Unit 14- Angles Date Lesson Topic Homework 3 W 5/16 1 Complementary Angles Lesson 1 - Page 5 4 T 5/17 2 Supplementary Angles Lesson 2 Page 9 5 F 5/18 3 Vertical Angles Lesson 3 Page 13 6 M 5/21 4 Mixed Angles Lesson 4- Pages T 5/22 Quiz 2 W 5/23 5 Parallel Lines- Day 1 Lesson 5- Pages T 5/24 SAGAMORE DAY! 4 F 5/25 6 Parallel Lines- Day 2 Lesson 6 Page 26 M 5/28 No School! T 5/29 Review Study! W 5/30 Test T 5/31 Field Trip! Name: # 1
2 Vocabulary: Lesson 1 Complementary Angles Angles 1) What is the vertex of the angle? 2) What are the two rays that make up the angle? and 3) What are the 4 names of the angle?,,, Complementary Angles - Complement - Perpendicular Lines - Equation for solving ALL complementary angle problems = Rules for Solving Complementary Angle Problems 1 - Choose Equation 2 - Substitute the information given 3 - Solve 4 - Answer the question Below are two examples of angles that are complementary. 2
3 Guided Practice: Find the missing angles. 1) Angles A and B are complementary find the measure of angle B. 2) 3) 4) 5) 6) m<1 : m<2 = 2 : 3 Find the measure of both angles. 1 2 Find the complement of the following angles: 7) 60 8) 18 9) 43 10) 89 11) x *12) The measure of a complement of an angle is 32 more than three times the angle. Find the two angles. 3
4 Problem Set: Solve for x: 1) 2) 3) Use the picture to the right for questions 4-7: 4) m<1 : m<2 = 8 : 1 5) m<1: m<2 = 19 : 11 Find the measure of <1 Find the measure of < ) m<1 : m<2 = 4 : 5 7) m<1 = 2x + 40, m<2 = 4x - 10 Find the measure of both angles Find the measure of <2 8) What is the complement of a 34 degree angle? 9) What is the complement of a 85 degree angle? 10) Find the measure of both angles. 5x 2x +20 4
5 Lesson 1 - Homework Find the measure of the complements of the following angles: 1) 32 2) 19 3) 54 4) ) 4x 6) 2x Use the picture to the right for questions 7 10: 7) m<1 = Find m<2. 8) m<2 = 8x, m<1 = x. Find m< ) m<1 = 2x + 10, m<2 = 4x ) m<1 : m<2 = 1 : 5 Find m<1 Find m<2 *11) The measure of an angle is 10 more than three times the measure of its complement. Find the measure of the larger angle. 5
6 Vocabulary: Lesson 2 Supplementary Angles Straight angle (Also known as angles on a line) - Supplementary angles - Supplement - Equation for solving ALL supplementary angle problems = Rules for Solving Supplementary Angle Problems 1 - Choose equation 2 - Substitute the information given 3 - Solve 4 - Answer the question Below are two examples of angles that are supplementary. Guided Practice: 1) If A and B are supplementary, find the m B 2) The following is a straight angle. A) Name the missing angle. B) Find the missing angle. 6
7 Find the missing angles. 3) 0 X 82 4) 7x 2x 5) 6) 4x 5x 15x x 7) Given: m 1 :m 2 = 8 : 1 Find: m 1 = m 2 = Find the measure of the supplements of angles with the given measures: 8) 62 9) ) 34 11) ) 8x 13) 11x *14) The measure of a supplement of an angle is 6 more than twice the measure of the angle. Find both angles. 7
8 Problem Set: Find the measure of the supplements of angles with the given measures: 1) 38 2) 134 3) 66 4) ) 7x 6) 14x For questions 7-9 use the diagram to the right ) m<2 = 55, Find m<1. 8) m<1 = 3x + 15, m<2 = 2x + 5 9) m<1 : m<2 = 7 : 3 Find m<1 Find both angles 10) Set up and solve an equation to find the value of x and then measures of both angles. 5x x ) Set up and solve an equation to find the value of x and then measures of both angles. 10x 2x *12) Two lines meet at the common vertex of two rays. Set up and solve the appropriate equations for m and n m n 8
9 Lesson 2 Homework 1. Find both angles in the diagram below: 2. Find both angles in the diagram below: *3. The measurement of an angle is 3 2 the measurement of its supplement. Find the measurement of the angle. 4. If <ABC & <ABD are supplementary and are in a ratio of 3:2, find the measure of <ABD. 5. Find the supplement of each of the following angles: a) 65 0 b) 90 0 c) d) 12 0 e) y 0 f) g) 4x 0 9
10 Lesson 3 Vertical Angles Vocabulary Vertical angles - When are vertical angles formed? Vertical angles are easily recognized in a diagram. They are the angles that are from each other. A picture of what that would look like is: According to this diagram, which angles would be classified as vertical?,. What other angle relationship have you learned already exists in the diagram as well? Equation for solving ALL vertical angle problems 1 = 2 Rules for Solving Vertical Angle Problems 1 - Choose Equation 2 - Substitute the information given 3 - Solve 4 - Answer the question Guided Practice: 1. Find all of the missing angles 2. Find all of the missing angles y x 42 0 z y x z x y z x y z 10
11 3. Find x and all of the angles 4. Find x and all of the angles y x z 2x + 40 x + 20 z y x y z x y z 5. Find x and all of the angles 6. Find x and all of the angles y 3x z 3x x + 10 z y x y z x y z 7. Three lines meet at a point. Set up and solve an equation to find the value of r. 34 r 122 Problem Set: 1) Are 1and 3 vertical angles? Why? 2) Name a pair of vertical angles. 11
12 3) Find the m 7 4) Find the m 8 5) Find the m 9 6) Find the m 10 7) Find the m 11 8) Find the m 12 9) If the m 1 = 65 Find the m 2 m 3 m 4 10) Given: m 1 = 120 m 3 = x Find the m 2 11) Given: m 4 = 50 m 2 = 3x + 20 Find x 12) Given: m 1 = 3x 10 m 2 = 140 Find the m 2 13) Three lines meet at a point. Set up and solve an equation to find the value of a and b. 78 b a 52 12
13 Lesson 3 Homework Use the picture below for questions 1-6. The picture is not drawn to scale! m<1 = m<2 = Find: m<2 Find: m<1 m<3 m<2 m<4 m<4 3. m<1 = 39 0, Find m<2, m<3 and m<4 4. m<2 = 112 0, Find m<1, m<3 and m<4 5. m<1 = x + 30, m<2 = 4x + 40, Find m<2. 6. m<1 = 85 0, m<3 = 4x + 5, solve for x. 7. Three lines meet at a point. In a complete sentence describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of y and z. z 19 y 13
14 Lesson 4 Mixed Practice of Complementary, Supplementary, and Vertical Angles Use the diagram below to answer questions 1-6 1) Given: FR FW 2) Given: AF AC 3) Given: AF AC m 1 = 34 o m BFW = 59 o m 1 = 4x + 5 Find the m 2 Find the m RFB m 2 = 2x + 15 Find the x 4) Given: AF AC 5) Given: AF AC 6) Given: AF AC m RFB = 3x + 20 m 1 : m 2 = 4 : 6 m 1 : m 2 = 2 : 7 m BFW = 2x + 20 Find the m 1 Find the m 1 Find the m BFW Use the diagram below to answer questions ) m 2 = 35 o 8) m 1 = 137 o 9) m 1 = 5x + 25 Find the m 1 Find the m 2 m 2 = x + 5 Find the x 14
15 10) m 1 = 3x ) m 1: m 2= 3:2 12) m 1: m 2= 7:3 m 2 = 2x - 20 Find the m 2 Find the m 1 Use the diagram below to answer questions ) m 1 = 3x - 20, m 2 = 64. find x 14) m 3 = 3x - 20, m 4 = 40. find the m 3 15) m 2 = 6x - 10, m 1 = 14. find the m 2 16) m 1 = 78, m 2 = 3x find the m 3 17) m 1 = 8x + 12, m 2 = 68. find the m 4 15
16 Lesson 4: Homework 1) What is the supplement of a 112º angle? 2) What is the complement of a 57º angle? 3) An angle measures 42º, what does an angle vertical to it measure? 4) If m ABD = 25º, what is the m CBD? 5) If angle 3 measures 134º, what does angle 4 measure? 6) If angle 3 measures 134º, what does angle 1 measure? 7) If angle DBC measures 124º, what does angle DBA measure? 8) 1 = 4x 25 3 = 19 Find the measure of 1 9) 1 = 4x 5 2 = x 10. Find the measure of 2 10) 1 = 4x 5 2 = x 10 Find the m 1. 16
17 A = 42º B = 116º C = 64º D = 48º 11) Which two angles are complementary? 12) Which two angles are supplementary? 13) Name a pair of congruent angles. 14) Name a pair of supplementary angles. 15) If 2 angles are complementary and one angle is 89º, find its complement. 16) If 2 angles are complementary and one angle is 5xº, find its complement. 17) If 2 angles are supplementary and one angle is 89º, find its supplement. 18) If 2 angles are supplementary and one angle is 5xº, find its supplement. 19) Two complementary angles are in a ratio of 3:12. Find each angle. 20) Two supplementary angles are in a 4:5 ratio. Find the larger angle. 17
18 Lesson 5 Parallel Lines Day 1 Think of and write down three examples of where parallel lines exist in the real world Words to know: Parallel Lines Perpendicular Lines Transversal Vertex 1 2 m 3 4 When 2 parallel lines are cut by a transversal 8 angles are formed. 5 6 n angles are acute 4 angles are obtuse p Angle Relationship Formed Supplementary Angles The 2 angles that make a straight line. They add to 180 o. Examples Vertical Angles The 2 angles opposite each other when 2 lines intersect. They are equal in measure. Corresponding Angles The 2 angles located in matching corners. They are equal in measure. Alternate Interior Angles The 2 angles located inside the parallel lines in opposite corners. They are equal in measure. Alternate Exterior Angles The 2 angles located outside the parallel lines in opposite corners. They are equal in measure. 18
19 Guided Practice: Use the following diagram to answer questions # 1 4. Not drawn to scale!! 1 2 m n 7 8 P 1) Give the measure of each angle if m<1 = 80 0 <2 = <3 = <4 = <5= <6 = <7= <8 = 2) Give the measure of each angle if m<3 = <1 = <2 = <4 = <5= <6 = <7= <8 = 3) Give the measure of each angle if m<8 = 75 0 <1 = <2 = <3 = <4= <5 = <6= <7 = 4) Give the measure of each angle if m<6 = <1 = <2 = <3 = <4= <5 = <7= <8 = 19
20 5) If m 4 = 105, find the m 6 8) If m 5 = 112, find the m 8 6) If m 3 = 35, find the m 6 9) If m 5 = 157, find the m 7 7) If m 8 = 124, find the m 1 10) If m 2 = 67, find the m 3 Problem Set: r 1) Which lines are the parallel lines? 2) Which line is the transversal? Name a pair of 3) Corresponding Angles 4) Alternate Interior Angles 5) Alternate Exterior Angles 6) Vertical Angles 7) Supplementary Angles 8) Give the measure of each angle if m 3 = ) Give the measure of each angle if m 8 = ) Give the measure of each angle if m 4 =
21 Use this diagram to answer the following questions Lesson 5 Homework a c b Classify each pair of angles: (Supplementary, vertical, corresponding, alternate interior, alternate exterior angles) 1. <1 and < 5 4. <5 and <8 2. <2 and <7 5. <3 and <6 3. <5 and <6 6. <1 and <4 7. Give the measure of each angle if m<2 = 45 0 <1 = <3 = <4 = <5= <6 = <7= <8 = 8. Give the measure of each angle if m <5 = <1 = <2 = <3 = <4= <6 = <7= <8 = 9. Give the measure of each angle if m<8 = <1 = <2 = <3 = <4= <5 = <6= <7 = 21
22 a b c 10. True or False: Angles 3 and 5 are congruent. 11. True or False: Angles 3 and 6 are congruent. 12. Name the parallel lines: 13. Name the transversal: 14. If m<5 = 95 0, fine m<8 15. If m<8 = 117 0, find m<4 16. If m<1 = 120 0, find m<8 17. If m<6 = 32 0, find m<3 18. True or False: 1 5? 19. True or False: 1 6? 20. True or False: 4 5? 22
23 Warm up: Lesson 6 Parallel Lines Day a b c 1. Give the measure of each angle if m<1 = <2 = <3 = <4 = <5= <6 = <7= <8 = 2. If m<4 = 100 0, find the m<1 4. If m<1 = 109 0, find the m<5 3. If m<3 = 120 0, find the m<6 5. If m<2 = 42 0, find the m<7 Rules for Solving Parallel Line Angle Problems = 1 - Choose Equation 2 - Plug in the information = 3 - Solve 4 - Answer the question + = 180 Guided Practice: a b c 1. If m<4 = 5x + 10 and m<8 = 120 0, solve for x 2. If m<3: m<4 = 4:5, solve for x 23
24 a b c 3. If m<1 = 3x + 20 and m<2 = x + 40, find m<2 4. If m<4: m<2 = 7:3, find m<2 5. If m<6 = 80 0 and m<7 = 2x + 20, find m <5 6. If m<2 = 4x 10 and m<6 = 70 0, find m<7 Problem Set: 1) Give the measure of each angle in m 1 = ) If m 4 = 95, find the m 1 4) If m 1 = 113, find the m 5 3) If m 3 = 60, find the m 6 5) If m 2 = 28, find the m 7 24
25 Solve algebraically: 6) If m 4 = 5x + 10 and the m 8 = 95, solve for x 7) If m 3 : m 4 = 4 : 5 Solve for x 8) If m 1 = 3x + 20 and the m 2 = x + 40, find m 2 9) If m 4 : m 2 = 7 : 3 Find the m 2 10) If m 6 = 98 and the m 7 = 2x + 20, find the m 5 25
26 Lesson 6 Homework G A E C B F D 1. Give the measure of each angle if m<aeg = 58 0 <GEC <AEF <CEF <BFE <DFE <BFH <HFD H 2. If m<bfh = 98 0, find m<dfh 3. If m<efd = 105 0, find m<gec 3. If m<aef = 72 0, find m<dfe 4. If m<bfh = 3x 10 and m<ceg = 110 0, solve for x. 5. If m<efb = 5x + 12 and m<cef = 132 0, find the measure of <EFB 6. If m<aeg = 3x 10 and m<gec = 2x + 40, find the measure of <DFH 7. True or False: Angles GEA and DFH are congruent? Which angle relationship exists? 26
27 Name: 7R Unit 15 Angles Review Sheet Matching - Definitions 1. A line that intersects parallel lines 2. Two angles whose sum measures 90degrees 3. Two pairs of opposite, congruent angles formed by intersecting lines. 4. Two lines that intersect to form 4 right angles. 5. Two lines in the same plane that never intersect. 6. Two angles whose sum measures 180 degrees 7. A pair of angles on opposite sides of the transversal inside the parallel lines Date: Math 7R a. complementary angles b. parallel lines c. vertical angles d. supplementary angles e. corresponding angles f. alternate interior angles g. transversal h. alternate exterior angles i. perpendicular lines 8. A pair of angles on opposite sides of the transversal outside the parallel lines 9. A pair of angles that occupy matching corners Lesson 1: Complementary Angles Find the missing angle: x 52 x 3x
28 Find the complement of the following angles: x x 0 For questions 19-20, use the picture to the right. 19. m<1 = 6x 20, m<2 = 4x Find m< m<1:m<2 = 4:11 Find the value of x 21. In a pair of complementary angles, the measurement of the larger angle is three times that of the smaller angle. Find the measurements of the two angles. Lesson 2: Supplementary Angles 22. Find the value of x 23. Find the measure of both angles 2X x x 28
29 Find the supplements of angles with the given measures: x For questions 28-30, use the diagram to the right m<1 = 5x, m<2 =15x 29. m<1 = 6x 10, m<2 = 3x + 10 Find the value of x. Find m < m<1 : m<2 = 4 : 5 Find the value of both angles. 31. The measures of two supplementary angles are in the ratio of 2:3. Find the two angles. 29
30 Lesson 3: Vertical Angles Use the picture below for questions The picture is not drawn to scale! m<2 = m<4 = Find: m<1 Find: m<1 m<3 m<2 m<4 m<3 34. m<1 = 39 0, Find m<2, m<3 and m<4 35. m<2 = 112 0, Find m<1, m<3 and m<4 36. m<1 = 3x + 30, m<2 = 66, solve for x. 37. m<1 = 3x, m<3 = x + 104, solve for x. 38. m<2 = 3x 20, m<3 = 130 0, find m< m<1 = 3x, m<3 = x + 64, find m<3. 30
31 Lesson 5&6: Parallel Lines Identify all of the angle relationships using the diagram below 5 6 m n 2 8 p 40. Supplementary 41. Vertical 42. Corresponding 43. Alternate Interior 44. Alternate Exterior 45. Which angle relationship does not result in the angles being congruent? Answer the following questions based on the above diagram and using algebra. 46. If m<7 : m<3 = 5 : 1, solve for the value of x. 47. If m<8 = 30 0, Find m< If m<2 = 125 0, Find m<6 49. If m<7 = 130 0, Find m<1 50. If m<1 = 6x 7 and m<5 = 6x + 43, find m< If m<3 = 55 0, Find m<1 31
32 51. a) Find the measure of ABC C 47 D b) Find the measure of DBE A B E c) Find the measure of ABE Review: 52. Factor 6x Solve for x: 2x + 3x + 5 = Simplify: 4x + 2(3x 6) If the radius of a circle is 5, what is the area in terms of pi? 32
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