Transcript Do Now 1.9.14 “Unusual Area” Javier is helping his uncle to tile a patio that has an irregular shape.

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.
NAME:______________________________ 1.9.14 Review Lesson
Learning Objective
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 multistep problem to write and solve simple equations for an unknown angle in a figure.
CFU
What are we going to do?
Activate Prior Knowledge
A right angle is an angle that measures 90.
A straight angle is an angle that measures 180.
Add the angle measures.
1.
2.
59
+ 31
90
59
31
Right angle
127.5
52.5

Straight angle
127.5
+ 52.5
180
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.
Concept Development 1
Properties1 of Angles
Complementary
Angles
Supplementary
Angles
m∠A + m∠B = 90°
m∠A + m∠B = 180°
Two angles are
complementary angles
if their sum is 90°.
Two angles are
supplementary angles
if their sum is 180°.
Complementary
Corner
CFU 1
How do you know that figure A
shows complementary angles?
Figure A shows complementary
angles because ____________.
68 + 22 = 90
How do you know that figure B
shows supplementary angles?
Figure B shows supplementary
113+ 67= 180
angles because ____________.
A
Supplementary
Straight
68
22
Complementary
B
113
67
Supplementary
57
33
119
61
60+ 30 = 90
125+ 55 = 180
57 is the complement of 33.
119 is the supplement of 61.
Go to Skill Dev 1
Vocabulary
1
distinctive feature of
Concept Development 2
Properties of Angles
Adjacent
Angles
Vertical
Angles
m∠A + m∠B = m∠C
m∠A = m∠B
Two angles are
adjacent angles
if they share a common
ray and endpoint.
Two angles are
vertical angles
if they are formed by two intersecting
lines and are not adjacent.
121.3
65
CFU 2
Which of the following figures
shows vertical angles?
How do you know?
A
B
Explain why the other figure
shows adjacent angles.
121.3
45
65+ 45= 110
121 = 121
Vertical angles share only a vertex.
The angle measures are equivalent.
Go to Skill Dev 2
Skill Development/Guided Practice 1
Complementary Angles
Supplementary Angles
m∠A + m∠B = 90°
m∠A + m∠B = 180°
Solve for unknown angle measures using properties of angles.
1 Determine2 the property of angles needed.
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.
3 Write the solution using the angle measure and degree symbol (m∠x = 45).
1. What is the measure of angle x?
m∠x = 57.5
32.5
1 How did I/you
determine the
property of angles
needed?
2 Once I/you substitute
the given angle
measure(s) into the
equation, how can I
solve for the missing
angle?
2. What is the measure of angle x?
m∠x + 58 = 90
- 58 - 58
m∠x = 32
m∠x + 32.5 = 90.0
- 32.5 - 32.5
x
CFU
x
58
complementary
Property of Angle: ______________
m∠x = 57.5
Measure: _____________________
3. What is the complement of a 38 angle?
m∠x + 38 = 90
- 38 - 38
m∠x = 52
complementary
Property of Angle: ______________
m∠x = 32
Measure: _____________________
4. What is the complement of an 13.5 angle?
m∠x + 13.5 = 90.0
- 13.5 -13.5
Vocabulary
2
m∠x = 76.5
3
figure out
replace
Skill Development/Guided Practice 1 (continued)
Complementary Angles
Supplementary Angles
m∠A + m∠B = 90°
m∠A + m∠B = 180°
Solve for unknown angle measures using properties of angles.
1 Determine the property of angles needed.
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.
3 Write the solution using the angle measure and degree symbol (m∠x = 45).
5. What is the measure of ∠1?
6. What is the measure of ∠2?
m∠1 + 106.7 = 180.0
m∠2 + 63.5 = 180.0
- 63.5 - 63.5
- 106.7 -106.7
106.7
1
m∠1 = 73.3
2
CFU
1 How did I/you
determine the
property of angles
needed?
2 Once I/you substitute
the given angle
measure(s) into the
equation, how can I
solve for the missing
angle?
m∠2 = 116.5
63.5
supplementary
Property of Angle: ______________
m∠1 = 73.3
Measure: _____________________
7. What is the supplement of a 120.4 angle?
m∠x + 120.4 = 180.0
- 120.4 - 120.4
m∠x = 59.6
supplementary
Property of Angle: ______________
m∠2 = 116.5
Measure: _____________________
8. What is the supplement of a 30.5 angle?
m∠x + 30.5 = 180.0
- 30.5 - 30.5
m∠x = 149.5
Go to
Concept Dev 2
Skill Development/Guided Practice 2
Adjacent Angles
Vertical Angles
m∠A + m∠B = m∠C
m∠A = m∠B
Solve for unknown angle measures using properties of angles.
1 Determine the property of angles needed.
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.
3 Write the solution using the angle measure and degree symbol (m∠x = 45).
9. What is the measure of angle x?
x
10. What is the measure of angle x?
127.3
x
71.5
35
71.5 + 35 = m∠x
106.5 = m∠x
42
m∠x + 42 = 127.3
- 42 - 42
m∠x = 85
adjacent
Property of Angle: ______________
m∠x = 106.5
Measure: _____________________
adjacent
Property of Angle: ______________
m∠x = 85.3
Measure: _____________________
CFU
1 How did I/you
determine the
property of angles
needed?
2 Once I/you substitute
the given angle
measure(s) into the
equation, how can I
solve for the missing
angle?
Skill Development/Guided Practice 2 (continued)
Adjacent Angles
Vertical Angles
m∠A + m∠B = m∠C
m∠A = m∠B
Solve for unknown angle measures using properties of angles.
1 Determine the property of angles needed.
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.
3 Write the solution using the angle measure and degree symbol (m∠x = 45).
11. What is the measure of angle x?
12. What is the measure of angle x?
x
75.7
88
x
88 = m∠x
vertical
Property of Angle: ______________
m∠x = 88
Measure: _____________________
m∠x = 75.7
vertical
Property of Angle: ______________
m∠x = 75.7
Measure: _____________________
CFU
1 How did I/you
determine the
property of angles
needed?
2 Once I/you substitute
the given angle
measure(s) into the
equation, how can I
solve for the missing
angle?
Skill Development/Guided Practice 2 (continued)
CFU
1 How did I/you determine what
the question is asking?
2 How did I/you determine the
math concept required?
3 How did I/you determine the
relevant information?
4 How did I/you solve and
interpret the problem?
5 How did I/you check the
reasonableness of the answer?
90°
Angle w is supplementary to
the sum of angles x & y
43°
Angle x is supplementary to
angle y
Angle w is vertical to the 43°
angle.
90°
Angle z is vertical to angle w. It
is also supplementary to x & y
47°
Relevance
Complementary Angles m∠A + m∠B = 90°
Supplementary Angles m∠A + m∠B = 180°
Adjacent Angles m∠A + m∠B = m∠C
Vertical Angles m∠A = m∠B
1 Solving for unknown angle measures using properties of angles will help
you solve real-world problems.
First St.
Baker St.
Baker St. intersects Main St. and First
St. forming two complementary angles.
If the orange car turns at a 43 angle,
at what angle will the red car turn?
x
Main St.
m∠x = 47
43
2 Solving for an unknown angle using properties of angles will help you
do well on tests.
CFU
Sample Test Question:
79. What is the supplement of a 25 angle?
A
B
C
D
65
135
155
165
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?
Complementary Angles m∠A + m∠B = 90°
Supplementary Angles m∠A + m∠B = 180°
Adjacent Angles m∠A + m∠B = m∠C
Vertical Angles m∠A = m∠B
Skill Closure
Solve for unknown angle measures using properties of angles.
1 Determine the property of angles needed.
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.
3 Write the solution using the angle measure and degree symbol (m∠x = 45).
1. What is the measure of angle x?
2. What is the measure of ∠1?
m∠1 + 115 = 180
- 115 - 115
m∠x + 53.5 = 90.0
- 53.5 - 53.5
x
m∠x = 36.5
53.5
complementary
Property of Angle: __________________
m∠x = 36.5
Measure: _____________________
115
1
supplementary
Property of Angle: __________________
m∠1 = 65
Measure: _____________________
Access Common Core
m∠A = 55
m∠B = 30
m∠C = 150
m∠D = 35
m∠1 = 65
Which two angles would form complementary angles?
How do you know? m∠A + m∠D = 90°
Which two angles would form supplementary angles?
How do you know? m∠A + m∠C = 180°
Word Bank
angle
complementary
supplementary
adjacent
vertical
unknown
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.
Independent Practice
Complementary Angles
Supplementary Angles
m∠A + m∠B = 90°
m∠A + m∠B = 180°
Adjacent Angles
Vertical Angles
m∠A + m∠B = m∠C
m∠A = m∠B
Solve for unknown angle measures using properties of angles.
1 Determine the property of angles needed.
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.
3 Write the solution using the angle measure and degree symbol (m∠x = 45).
1. What is the measure of ∠1?
27.3
1
2. What is the measure of angle x?
m∠1 + 27.3 = 90.0
- 27.3 -27.3
x
128.5
m∠x + 128.5 = 180.0
- 128.5 -128.5
m∠1 = 62.7
complementary
Property of Angle: ______________
Measure: _____________________
m∠1 = 62.7
3. What is the complement of a 51.4 angle?
m∠x + 51.4 = 90.0
- 51.4 - 51.4
m∠x = 38.6
m∠x = 51.5
supplementary
Property of Angle: ______________
Measure: _____________________
m∠x = 51.5
4. What is the supplement of a 62.6 angle?
m∠x + 62.6 = 180.0
- 62.6 - 62.6
m∠x = 117.4
Independent Practice (continued)
Complementary Angles
Supplementary Angles
m∠A + m∠B = 90°
m∠A + m∠B = 180°
Adjacent Angles
Vertical Angles
m∠A + m∠B = m∠C
m∠A = m∠B
Solve for unknown angle measures using properties of angles.
1 Determine the property of angles needed.
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.
3 Write the solution using the angle measure and degree symbol (m∠x = 45).
5. What is the measure of angle x?
x
6. What is the measure of angle x?
x
85.3
40
117
85.3 + 40 = m∠x
125.3 = m∠x
adjacent
Property of Angle: ______________
m∠x = 125.3
Measure: _____________________
m∠x = 117
vertical
Property of Angle: ______________
m∠x = 117
Measure: _____________________
Independent Practice (Cont.)
1. What is the measure of angle x?
34.3° + m∠x = 90.0°
– 34.3°
– 34.3°
m∠x = 55.7°
75°
y
2. What is the measure of angle y?
x
34.3°
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°.
x
79°
Xavier thinks that the measure of angle y is 89.5°.
Explain the mistake he made.
Xavier confused vertical angles with supplementary angles.
Angle y should be 90.5° because vertical angles are equal in measure.
90.5°
y
Homework
Hint:
X + X = 90
m∠x + 37 = 90
- 37 - 37
m∠x = 53
m∠x + 51 = 90
- 51 - 51
m∠x = 39
m∠x + m∠x  = 90
2x = 90
m∠x = 45
Hint:
X + 2X = 180
m∠x + 116 = 180
- 116 - 116
m∠x = 64
m∠x + 34 = 180
- 34 - 34
m∠x = 146
m∠x + m∠2x = 180
3x = 180
m∠x = 60
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°
132°
48°
48°
Angle x is vertical to the
132° angle.
Angle y is supplementary to
the 132° angle.
Angle z is vertical to angle y. It is also
supplementary to the 132° angle.
149°
31°
90°
Angle w is vertical to angle y.
Angle x is supplementary to
either angle w or angle y.
Angle y is supplementary to
the 59° angle.
Angle z is given as a 90°
(right) angle.