Do Now 1.9.14 “Unusual Area”

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.

What are we going to do?

CFU

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.

Make Connection

We will solve for an unknown angle using properties of angles.

Learning Objective

Activate Prior Knowledge

A right angle is an angle that measures 90.A straight angle is an angle that measures 180.

Right angle Straight angle

59+ 31

90

127.5+ 52.5

18031

59 52.5

127.5

1. 2.

Add the angle measures.

7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

NAME:______________________________ 1.9.14 Review Lesson

ComplementaryAngles

SupplementaryAngles

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°.

6111933

57

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 1

1 distinctive feature of

Vocabulary

Concept Development 1

Properties1 of Angles

ComplementaryCorner

60+ 30 = 90

57 is the complement of 33.

SupplementaryStraight

Go to Skill Dev 1

6822

A

Complementary

67113

B

Supplementary

68 + 22 = 90

113+ 67= 180

125+ 55 = 180

119 is the supplement of 61.

AdjacentAngles

VerticalAngles

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.

4565

Concept Development 2

Properties of Angles

65+ 45= 110

121.3

121.3

121 = 121

Which of the following figures shows vertical angles? How do you know?

Explain why the other figure shows adjacent angles.

CFU 2

A

B

Go to Skill Dev 2

Vertical angles share only a vertex.

The angle measures are equivalent.

Can adjacent angles also be vertical?

1. What is the measure of angle x? 2. What is the measure of angle x?

3. What is the complement of a 38 angle? 4. What is the complement of an 13.5 angle?

Determine2 the property of angles needed.Solve for the unknown angle measure using the property of angles as follows:

Substitute3 the given angle measure(s) into the equation.Solve the equation.

Write the solution using the angle measure and degree symbol (m∠x = 45).

Solve for unknown angle measures using properties of angles.1

2

3

ab

2 figure out3 replace

Vocabulary

How did I/you determine the property of angles needed?

Once I/you substitute the given angle measure(s) into the equation, how can I solve for the missing angle?

CFU

1

2

Complementary Angles

m A + ∠ m B = 90°∠

Supplementary Angles

m A + ∠ m B = 180°∠

x5832.5

x

Property of Angle: ______________

Measure: _____________________

complementary Property of Angle: ______________

Measure: _____________________

m∠x + 32.5 = 90.0- 32.5 - 32.5

m∠x = 57.5

m∠x = 57.5

complementary

m∠x + 58 = 90- 58 - 58m∠x = 32

m∠x = 32

m∠x + 38 = 90- 38 - 38

m∠x = 52

m∠x + 13.5 = 90.0- 13.5 -13.5

m∠x = 76.5

Skill Development/Guided Practice 1

Skill Development/Guided Practice 1 (continued)

Go to Concept Dev 2

Determine the property of angles needed.Solve for the unknown angle measure using the property of angles as follows:

Substitute the given angle measure(s) into the equation.Solve the equation.



2

3

ab

5. What is the measure of 1?∠ 6. What is the measure of 2?∠

7. What is the supplement of a 120.4 angle? 8. What is the supplement of a 30.5 angle?

1106.7 63.5

2


Measure: _____________________

supplementary Property of Angle: ______________

Measure: _____________________

m∠1 + 106.7 = 180.0

- 106.7 -106.7

m∠1 = 73.3

m∠1 = 73.3supplementary

m∠2 + 63.5 = 180.0- 63.5 - 63.5

m∠2 = 116.5

m∠2 = 116.5

m∠x + 120.4 = 180.0- 120.4 - 120.4

m∠x = 59.6

m∠x + 30.5 = 180.0- 30.5 - 30.5

m∠x = 149.5


m A + ∠ m B = 90°∠


m A + ∠ m B = 180°∠



CFU

1

2


Measure: _____________________


Measure: _____________________

Adjacent Angles

m A + ∠ m B = ∠ m C∠

Vertical Angles

m A = ∠ m B∠





2

3

ab

Skill Development/Guided Practice 2


adjacent

- 42 - 42

m∠x = 85

m∠x = 85.3

m∠x + 42 = 127.3

adjacent

71.5 + 35 = m∠x

m∠x = 106.5

106.5 = m∠x

71.535

x 127.3

42x



CFU

1

2






2

3

ab



Measure: _____________________


Measure: _____________________m∠x = 75.7

m∠x = 75.7

vertical

88 = m∠x

m∠x = 88

88

x

75.7x

vertical

Adjacent Angles

m A + ∠ m B = ∠ m C∠

Vertical Angles

m A = ∠ m B∠



CFU

1

2


How did I/you determine what the question is asking?How did I/you determine the math concept required?How did I/you determine the relevant information?How did I/you solve and interpret the problem?How did I/you check the reasonableness of the answer?

CFU

2

1

3

4

5

90° Angle w is supplementary to

the sum of angles x & y

43° Angle w is vertical to the 43°

angle.

47° Angle x is supplementary to angle y

90° Angle z is vertical to angle w. It is also supplementary to x & y

Solving for unknown angle measures using properties of angles will help you solve real-world problems.

Solving for an unknown angle using properties of angles will help you do well on tests.

1

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?

CFU

2

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∠

Sample Test Question:

79. What is the supplement of a 25 angle?

A 65 B 135 C 155 D 165

43

x

Baker St.

Main St.

First 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?

m∠x = 47

__





2

3

ab

What did you learn today about solving for unknown angle measures using properties of angles? (Pair-Share) Use words from the word bank.

Skill Closure

Access Common Core

Summary Closure

Word Bankangle

complementarysupplementary

adjacentvertical

unknown

1. What is the measure of angle x?

Property of Angle: __________________Measure: _____________________

2. What is the measure of 1?∠

Property of Angle: __________________Measure: _____________________

x53.5

1115

complementary

m∠x + 53.5 = 90.0- 53.5 - 53.5

m∠x = 36.5

m∠x = 36.5supplementary

m∠1 + 115 = 180- 115 - 115

m∠1 = 65

m∠1 = 65

Which two angles would form complementary angles? How do you know?Which two angles would form supplementary angles? How do you know?

m A = 55∠ m B = 30∠ m C = 150∠ m D = 35∠

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∠

m A + ∠ m D = 90°∠

m A + ∠ m C = 180°∠

27.31

Independent Practice

1. What is the measure of 1?∠ 2. What is the measure of angle x?

3. What is the complement of a 51.4 angle? 4. What is the supplement of a 62.6 angle?

x 128.5


Measure: _____________________


Measure: _____________________

complementary

m∠1 + 27.3 = 90.0- 27.3 -27.3

m∠1 = 62.7

m∠1 = 62.7supplementary

m∠x + 128.5 = 180.0- 128.5 -128.5

m∠x = 51.5

m∠x = 51.5

m∠x + 51.4 = 90.0- 51.4 - 51.4

m∠x = 38.6

m∠x + 62.6 = 180.0- 62.6 - 62.6

m∠x = 117.4





2

3

ab

Adjacent Angles

m A + ∠ m B = ∠ m C∠

Vertical Angles

m A = ∠ m B∠


m A + ∠ m B = 90°∠


m A + ∠ m B = 180°∠





2

3

ab

Adjacent Angles

m A + ∠ m B = ∠ m C∠

Vertical Angles

m A = ∠ m B∠


m A + ∠ m B = 90°∠


m A + ∠ m B = 180°∠



Measure: _____________________


Measure: _____________________

adjacent

85.3 + 40 = m∠x

m∠x = 125.3

125.3 = m∠x

85.340

x

Independent Practice (continued)

m∠x = 117

m∠x = 117

117

x

vertical

Independent Practice (Cont.)

Access Common Core

1. What is the measure of angle x?

2. What is the measure of angle y?

34.3° + m∠x = 90.0°– 34.3°– 34.3°

m∠x = 55.7°

34.3° = m∠y (They are Vertical Angles)

34.3° = 34.3°

y34.3°

x75°

Felicia thinks that the measure of angle x is 16°. Explain the mistake she made.

x 79°

Xavier thinks that the measure of angle y is 89.5°. Explain the mistake he made.

90.5° y

Felicia confused supplementary angles with complementary angles. The sum of x and 79° should be 180°, not 90°.

Xavier confused vertical angles with supplementary angles. Angle y should be 90.5° because vertical angles are equal in measure.

Homework

- 37 - 37

m∠x = 53

m∠x + 37 = 90- 51 - 51

m∠x = 39

m∠x + 51 = 902x = 90

m∠x = 45

m∠x + m∠x = 90

- 116 - 116

m∠x = 64

m∠x + 116 = 180- 34 - 34

m∠x = 146

m∠x + 34 = 180 3x = 180

m∠x = 60

m∠x + m 2∠ x = 180

Hint:

X + X = 90

Hint:

X + 2X = 180

Homework

Use your knowledge of vertical angles, supplementary angles, complementary angles, and adjacent angles to determine the unknown angles for each figure below.

48° Angle y is supplementary to

the 132° angle.

132° Angle x is vertical to the 132° angle.

48° Angle z is vertical to angle y. It is also supplementary to the 132° angle.

31° Angle y is supplementary to the 59° angle.

HINT: It may be necessary to solve for variables (not in alphabetical order)

31° Angle w is vertical to angle y.

149° Angle x is supplementary to

either angle w or angle y.

90° Angle z is given as a 90° (right) angle.

Do Now 1.9.14 “Unusual Area”

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