Download supplementary angles

Name ___________________________
Learning Objective
Today, we will solve for unknown angle measures using properties of angles.
* Pre-requisite: AF 1.1 Solving one-step equation
CFU
What are we going to do today?
Activate (or provide) Prior Knowledge
A right angle is an angle that measures 90º.
A straight angle is 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°
30°
Right angle
60°
+ 30°
90°
125°
55°
125°
+ 55°
180°
Straight 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.
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Concept Development
Properties1 of Angles
1 facts
about something
Complementary
Angles
Supplementary
Angles
mA + mB = 90o
mA + mB =180o
Two angles are
complementary angles
if their sum is 90º.
Two angles are
supplementary angles
if their sum is 180º.
Interior Angles
of a Triangle
mA + mB + mC =180o
The sum of the
three interior2 angles
of a triangle is 180º.
2
Complementary
Corner
60°
B
Supplementary
Straight
125°
30°
60°+ 30° = 90°
70°
55°
60°
125°+ 55° = 180°
60º is the complement of 30º.
inside
50°
A
C
60°+ 70°+ 50° = 180°
125º is the supplement of 55º.
CFU #1
How do you know that figure A shows complementary angles?
Figure A shows complementary angles because ______________.
70° + 20° = 90°
How do you know that figure B shows supplementary angles?
115°+ 65° = 180°
Figure B shows supplementary angles because ______________.
Go To Skill
Dev #1
A
Go To Skill
Dev #2
B
70°
20°
Complementary
115°
65°
Supplementary
CFU #2
The following three angles cannot form a triangle: 40°, 30°, and 100°. Explain why.
DataWORKS Educational Research
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40° + 30° + 100° ≠ 180°
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice 1
Solve for unknown angle measures using properties of angles.
Complementary
Angles
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 90o
mA + mB = 180o
mA + mB + mC = 180o
Determine2
Step #1:
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 ( mx  45).
2
3
figure out
replace
1. What is the measure of angle x?
2. What is the measure of angle x?
mx + 35 = 90
-35 -35
x
mx = 55
35°
complementary
Property of Angle: __________________
Measure: _____________________
mx  55
3. What is the complement of a 19° angle?
mx +19 = 90
-19 -19
mx = 71
mx + 50 = 90
-50 -50
mx = 40
x
50°
complementary
Property of Angle: __________________
Measure: _____________________
mx  40
4. What is the complement of an 85° angle?
mx + 85 = 90
-85 -85
mx = 5
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?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice 1 (continued)
Solve for unknown angle measures using properties of angles.
Complementary
Angles
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 90o
mA + mB = 180o
mA + mB + mC = 180o
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 ( mx  45).
5. What is the measure of angle 1?
110°
1
6. What is the measure of angle 2?
m1 + 110 = 180
-110 -110
supplementary
Property of Angle: __________________
Measure: _____________________
m1  70
7. What is the supplement of a 125° angle?
m1 = 70
2
supplementary
Property of Angle: __________________
Measure: _____________________
m1  112
8. What is the supplement of a 30° angle?
mx + 30 = 180
-30 -30
mx = 150
-125 -125
mx = 55
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?
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Comments? [email protected]
m2 = 112
68°
mx +125 = 180
DataWORKS Educational Research
m2 + 68 = 180
-68 -68
Return to
Concept
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice 2
Complementary
Angles
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 90o
mA + mB = 180o
mA + mB + mC = 180o
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 ( mx  45).
9. What is the measure of angle x?
x
75°
x
10. What is the measure of angle x?
56°
94°
35°
mx + 75 + 35 = 180
mx + 94 + 56 = 180
mx + 110 = 180
-110 -110
mx + 150 = 180
-150 -150
mx = 30
mx = 70
angles of a triangle
Property of Angle:interior
__________________
mx  30
Measure: _____________________
interior angles of a triangle
Property of Angle: __________________
mx  70
Measure: _____________________
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?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice 2 (continued)
Solve for unknown angle measures using properties of angles.
Complementary
Angles
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 90o
mA + mB = 180o
mA + mB + mC = 180o
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 ( mx  45).
11. What are the measures of angles x, y, and z?
12. What are the measures of angles x, y, and z?
mx + 35 + 95 = 180
mx + 130 = 180
35°
y
x
95°
z
–130 –130
mx = 50
mx + 150 = 180
x
–150 –150
mx = 30
y
z
my + 50 = 90
mz + 95 = 180
–50 –50
–95 –95
mz = 85
my = 40
mx + 60 + 90 = 180
60°
my + 30 = 180
–30
my
mx  50
my  40
mz + 150 = 180
–30
= 150
–150 –150
mz = 30
mx
 30
my  150
mz  30
Measures: _____________________
mz  85
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?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Relevance
Complementary
Angles
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 90o
mA + mB = 180o
mA + mB + mC = 180o
1. Solving for unknown angle measures using
properties of angles will prepare you to
solve more difficult geometry problems.
2. Solving for unknown angle measures using
properties of angles will help you do well on
tests.
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.
1
2
( x )  (3 x  30)  90
4 x  30  90
4 x  60
x  15
Angle 1 = x
so, m 1 = 15°
Angle 2 = 3x + 30°
= 3(15°)+30°
= 45°+30°
so, m  2= 75°
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?
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Complementary
Angles
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 90o
mA + mB = 180o
mA + mB + mC = 180o
Skill Closure
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 ( mx  45).
1. What is the measure of angle x?
mx
x
48°
2. What is the measure of angle 1?
m1 +108 = 180
+ 48 = 90
-48
-48
mx
= 42
Property of Angle: complementary
__________________
mx  42
Measure: _____________________
-108
108°
1
-108
m1 = 72
supplementary
Property of Angle: __________________
Measure: _____________________
m1  72
Constructed Response Closure
m A  50
m B  30
m C  130
m D  40
Summary 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?
______________________________________________________________________
______________________________________________________________________
What did you learn today about solving for unknown angle measures using properties of angles?
Day 1 ______________________________________________________________________
Day 2 ______________________________________________________________________
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Name ________________________________
Independent Practice
Complementary
Angles
Solve for unknown angle measures using properties of angles.
mA + mB = 90o
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 180o
mA + mB + mC = 180o
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 ( mx  45).
1. What is the measure of angle 1?
1
2. What is the measure of angle x?
25°
136°
x
m1 + 25 = 90
mx +136 = 180
-25
-25
-136
m1
= 65
mx
complementary
Property of Angle: __________________
m1  65
Measure: _____________________
3. What is the complement of a 51° angle?
-136
= 44
supplementary
Property of Angle: __________________
Measure: _____________________
mx  44
4. What is the supplement of a 62° angle?
mx + 51= 90
mx + 62 = 180
-51 -51
mx = 39
-62 -62
mx = 118
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Independent Practice (continued)
Complementary
Angles
Solve for unknown angle measures using properties of angles.
mA + mB = 90o
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 180o
mA + mB + mC = 180o
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 ( mx  45).
5. What is the measure of angle 1?
6. What are the measures of angles x, y, and z?
105°
40°
z
35 y
28°
x
mx + 28 = 90
-28 -28
mx = 62
m1 + 65 + 35 = 180
m1 +100 = 180
-100 -100
m1 = 80
Property of Angle: interior
__________________
angles of a triangle
m

1

80

Measure: _____________________
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
my + 40  105 = 180
my + 145 = 180
mz + 35 = 180
-145 -145
my = 35
mz = 145
-35
-35
mx
my
 62
 35
mz  145
Measures: ________________________
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Name ________________________________
Periodic Review 1
Complementary
Angles
Solve for unknown angle measures using properties of angles.
mA + mB = 90o
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 180o
mA + mB + mC = 180o
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 ( mx  45).
1. What is the measure of angle x?
mx
23°
x
+ 23 = 90
-23
-23
m x
= 67
2. What is the measure of angle 1?
1
69°
complementary
Property of Angle: __________________
mx  67
Measure: _____________________
3. What are the measures of angles x and y?
28° mx + 28 = 180
-28
-28
mx = 152
x
72°
my + 72 = 90
-72 -72
my = 18
y
5. What is the supplement of a 75° angle?
mx + 75 = 180
mx = 105
-75 -75
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
-69
-69
m1
= 111
supplementary
Property of Angle: __________________
m1  111
Measure: _____________________
4. What are the measures of angles 1 and 2?
m1 + 52  90 = 180
m1 + 142 = 180
-142 -142
52°
m1 = 38
33°
2
mx  152 my  18
Measures: _____________________
m1 + 69 = 180
m2 + 33 = 90
-33 -33
m2 = 57
1
m1  38 m2  57
Measures: _____________________
6. What is the complement of a 41° angle?
mx + 41= 90
mx = 49
-41 -41
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Name ________________________________
Periodic Review 2
Complementary
Angles
Solve for unknown angle measures using properties of angles.
mA + mB = 90o
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 180o
mA + mB + mC = 180o
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 ( mx  45).
1. What are the measures of angles 1 and 2?
38°
m1 + 38 = 90
1
-38 -38
m2 + 52 = 90
-52 -52
m2 = 38
m1 = 52
52°
2. What are the measures angles of x and y?
mx + 40 = 180 my + 140 = 180
-140 -140
-40 -40
40°
x
my = 40
y
140°
mx = 140
2
mx  140 my  40
Measures: _____________________
m1  52 m2  38
Measures: _____________________
3. What are the measures of angles 1, 2, and 3?
48°
2
1
3
m3 + 42 = 180
-42
m2 + 48 + 90 = 180
m1 + 48 = 90
-48 -48
m1 = 42
m2 + 138 = 180
-138 -138
m2 = 42
-42
m3 = 138
30°
m1  42
m2  42
m3  138
Measures: ________________________
5. What is the supplement of a 1° angle?
mx +1= 180
mx = 179
-1
-1
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4. What are the measures of angles x, y, and z?
mz + 30  42 = 180
48° my + 138 = 180 mz + 72 = 180
42y
-72 -72
-138 -138
x 138˚
z
22°
my = 42
mz = 108
mx + 22 = 90
-22 -22
mx = 68
 68
 42
mz  108
Measures: _________________________
mx
my
6. What is the complement of a 1° angle?
mx +1= 90
mx = 89
-1 -1
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
Name ________________________________
Periodic Review 3
Complementary
Angles
Solve for unknown angle measures using properties of angles.
mA + mB = 90o
Supplementary
Angles
Interior Angles of
a Triangle
mA + mB = 180o
mA + mB + mC = 180o
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 ( mx  45).
1. What are the measures of angles x and y?
mx + 47 = 90
47°
my + 53 = 90
-53 -53
-47 -47
mx = 43
53°
x
2. What are the measures of angles 1, 2, and 3?
my = 37
m2 + 67 = 90
71°
3
2
y
67°
-67 -67
1
z
154°
mx + 51  90 = 180
mx +141= 180
-141 -141
mx = 39
-154 -154
my = 26
x
y
-37 -37
mz = 53
115° 1
3 2 55°
65°
mx  39
my  26
mz  53
Measures: _____________________
5. What is the supplement of a 34° angle?
mx + 34 = 180
mx = 146
-34 -34
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m3 = 19
4. What are the measures of angles 1, 2, and 3?
my + 154 = 180 mz + 37 = 90
37° 51°
m2 = 23
-71 -71
m1  90
m2  23
Measures: _________________________
m3  19
mx  43 my  37
Measures: _____________________
3. What are the measures of angles x, y, and z?
m3 + 71 = 90
55°
m1 + 115 = 180
-115 -115
m1 = 65
m2 + 65 + 55 = 180 m3 + 115 = 180
m2 + 120 = 180
-120 -120
m2 = 60
-115 -115
m3 = 65
m1  65
m2  60
m3  65
Measures: ____________________
6. What is the complement of a 76° angle?
mx + 76 = 90
mx = 14
-76 -76
6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.
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6th Grade Measurement and Geometry 2.2 (4Q)
Use the properties of complementary and supplementary angles and the sum of
the angles of a triangle to solve problems involving an unknown angle.
Lesson to be used by EDI-trained teachers only.