Download 6th_MA_MG_2.2_COMP_SUPP_ANGLES_DW

Name _____________________
L ea rn i n g Obj e cti v e
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?
Acti va t e ( o r p r o vi de ) P ri o r K n o wl edg e
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
125°
55°
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
(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.
Co n c e pt D ev el opm e n t
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°
70°
55°
125°+ 55° = 180°
60° + 30° = 90°
60º is the complement of 30º.
125º is the supplement of 55º.
Go To Skill
Dev #1
A
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.
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
inside
60°
50°
A
C
60°+ 70°+ 50° = 180°
Go To Skill
Dev #2
B
115°
70°
20°
Complementary
65°
Supplementary
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.
Ski l l Dev el o pm en t /G u i ded P ra cti c e 1
Complementary
Angles
mA + mB = 90o
Supplementary
Angles
mA + mB = 180o
Interior Angles
of a Triangle
mA + mB + mC = 180o
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 ( mx  45 ).
2 figure
3
out
replace
1. What is the measure of angle x?
Property of Angle: __________________
x
Measure: __________________
35°
2. What is the measure of angle x?
x
Property of Angle: __________________
50°
Measure: __________________
3. What is the complement of a 19° angle?
4. What is the complement of an 85° angle?
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.
Ski l l Dev el o pm en t /G u i ded P ra cti c e 1 ( c o n ti n u ed)
Complementary
Angles
mA + mB = 90o
Supplementary
Angles
mA + mB = 180o
Interior Angles
of a Triangle
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 ).
5. What is the measure of angle 1?
1
110°
Property of Angle: __________________
Measure: __________________
6. What is the measure of angle 2?
2
68°
Property of Angle: __________________
Measure: __________________
7. What is the supplement of a 125° angle?
8. What is the supplement of a 30° angle?
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?
6th Grade Measurement and Geometry 2.2 (4Q)
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
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.
Ski l l Dev el o pm en t /G u i ded P ra cti c e 2
Complementary
Angles
mA + mB = 90o
Supplementary
Angles
mA + mB = 180o
Interior Angles
of a Triangle
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?
75°
x
10. What is the measure of angle x?
x
56°
35°
94°
Property of Angle: __________________
Measure: __________________
Property of Angle: __________________
Measure: __________________
11. What are the measures of angles x, y, and z?
35°
y
x
95°
z
Measures: ____________________
12. What are the measures of angles x, y, and z?
60°
x
y
z
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.
Rel e va n c e
Complementary
Angles
mA + mB = 90o
Supplementary
Angles
mA + mB = 180o
Interior Angles
of a Triangle
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.
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  A = 15°
Angle 2 = 3x + 30°
= 3(15°)+30°
= 45°+30°
so, m  2= 75°
2. Solving for unknown angle measure using properties of angles will
help you do well on tests.
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
(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.
Complementary
Angles
mA + mB = 90o
Supplementary
Angles
mA + mB = 180o
Interior Angles
of a Triangle
mA + mB + mC = 180o
Ski l l Cl osu r e
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?
x
2. What is the measure of angle 1?
108°
48°
1
Property of Angle: ___________________
Property of Angle: ___________________
Measure: ______________________
Measure: ______________________
Co n st ru ct e d R e sp on s e Cl o su r e
m A  50
m B  30
m C  130
m D  40
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?
______________________________________________________
______________________________________________________
Su mm ar y Cl o su r e
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 _____________________
In d ep en d en t P ra cti c e
Complementary
Angles
mA + mB = 90o
Supplementary
Angles
mA + mB = 180o
Interior Angles
of a Triangle
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 ).
1. What is the measure of angle 1?
1
25°
Property of Angle: ___________________
Measures: ______________________
2. What is the measure of angle x?
136°
x
Property of Angle: ___________________
Measures: ______________________
3. What is the complement of a 51° angle? 4. What is the supplement of a 62° angle?
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 _____________________
In d ep en d en t P ra cti c e ( co n ti n u ed)
Complementary
Angles
mA + mB = 90o
Supplementary
Angles
mA + mB = 180o
Interior Angles
of a Triangle
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 ).
5. What is the measure of angle 1?
65°
35°
1
Property of Angle: ___________________
Measures: ______________________
6. What is the measure of angles x, y and z?
105°
40°
z
y
28°
x
Property of Angle: ___________________
Measures: ______________________
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 _____________________
P eri odi c R evi ew 1
Complementary
Angles
Supplementary
Angles
mA + mB = 90o
mA + mB = 180o
Interior Angles
of a Triangle
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 ).
1. What is the measure of angle x?
23°
x
Property of Angle: ___________________
Measure: ______________________
2. What is the measure of angle 1?
1
69°
Property of Angle: ___________________
Measure: ______________________
3. What are the measures of angles x and y?
28°
x
72°
y
Measures: ______________________
4. What are the measures of angles 1 and 2?
52°
33°
2
1
Measures: ______________________
5. What is the supplement of a 75° angle?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6. What is the complement of a 41° angle?
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 _____________________
P eri odi c R evi ew 2
Complementary
Angles
mA + mB = 90o
Supplementary
Angles
mA + mB = 180o
Interior Angles
of a Triangle
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 ).
1. What are the measures of angles 1 and 2?
38°
1
52°
2
Measures: ______________________
2. What are the measures of angles x and y?
40°
x
y
140°
Measures: ______________________
3. What are the measures of angles 1, 2, and 3?
1
2
48°
3
Measures: ______________________
4. What are the measures of angles x, y, and z?
y
z
48°
x
22°
30°
Measures: ______________________
5. What is the supplement of a 1° angle?
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6. What is the complement of a 1° angle?
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 _____________________
P eri odi c R evi ew 3
Complementary
Angles
mA + mB = 90o
Supplementary
Angles
mA + mB = 180o
Interior Angles
of a Triangle
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 ).
1. What are the measures of angles x and y?
47°
53°
Measures: ______________________
y
x
2. What are the measures of angles 1, 2, and 3?
71°
3
2
67°
1
Measures: ______________________
3. What are the measures of angles x, y, and z?
37°
51°
x
z
y
154°
Measures: ______________________
4. What are the measures of angles 1, 2, and 3?
115° 1
3 2 55°
65°
55°
Measures: ______________________
5. What is the supplement of a 34° angle?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6. What is the complement of a 76° angle?
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.