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7•3
Lesson 7
FUSD AZCCRS MATHEMATICS CURRICULUM
Lesson 7: Angle Problems and Solving Equations
Classwork
Angle Facts and Definitions
Name of Angle
Relationship
Angle Fact
Diagram
B
Adjacent Angles
C
a°
b°
A
D
D
G
a°
Vertical Angles
(vert. ∠s)
b°
C
F
E
C
Angles on a
Line
(∠s on a line)
a°
b°
B
A
D
B
Angles at a
Point
(∠s at a point)
a°
b°
A
D
c°
C
Use the diagram to complete the chart.
Name the angles that are …
Vertical
Adjacent
Angles on a line
Angles at a point
Lesson 7:
Angle Problems and Solving Equations
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M3-TE-1.3.0-08.2015
S.20
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
7•3
Lesson 7
FUSD AZCCRS MATHEMATICS CURRICULUM
Example 1
Estimate the measurement of 𝑥. ________
In a complete sentence, describe the angle relationship in the diagram.
Write an equation for the angle relationship shown in the figure and solve for 𝑥.
Exercise 1
In a complete sentence, describe the angle relationship in the diagram.
C
D
Find the measurements of ∠𝐵𝐴𝐶 and ∠𝐷𝐴𝐸.
3x°
2x°
A
B
E
Example 2
In a complete sentence, describe the angle relationship in the diagram.
Write an equation for the angle relationship shown in the figure and solve for 𝑥
and 𝑦. Find the measurements of ∠𝐿𝐸𝐵 and ∠𝐾𝐸𝐵.
Exercise 2
In a complete sentence, describe the angle relationships in the diagram.
N
16° M
J
3x°
Write an equation for the angle relationship shown in the figure and solve for 𝑥.
E
85°
K
Lesson 7:
Angle Problems and Solving Equations
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M3-TE-1.3.0-08.2015
L
S.21
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 7
FUSD AZCCRS MATHEMATICS CURRICULUM
7•3
Example 3
In a complete sentence, describe the angle relationships in the diagram.
E
Write an equation for the angle relationship shown in the figure and solve for 𝑥. Find the
measurement of ∠𝐸𝐾𝐹.
x°
G
K
135°
F
Exercise 3
In a complete sentence, describe the angle relationships in the diagram.
Find the measurement of ∠𝐺𝐴𝐻.
Example 4
The following two lines intersect. The ratio of the measurements of the obtuse angle to
the acute angle in any adjacent angle pair in this figure is
2 ∶ 1. In a complete sentence, describe the angle relationships in the diagram.
Label the diagram with expressions that describe this relationship. Write an equation
that models the angle relationship and solve for 𝑥. Find the measurements of the acute
and obtuse angles.
Exercise 4
The ratio of 𝑚∠𝐺𝐹𝐻 to 𝑚∠𝐸𝐹𝐻 is 2 ∶ 3. In a complete sentence, describe the angle relationships in the diagram.
Find the measures of ∠𝐺𝐹𝐻 and ∠𝐸𝐹𝐻.
Lesson 7:
Angle Problems and Solving Equations
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M3-TE-1.3.0-08.2015
S.22
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
7•3
Lesson 7
FUSD AZCCRS MATHEMATICS CURRICULUM
Relevant Vocabulary
⃗⃗⃗⃗⃗ are adjacent angles if 𝐶 belongs to the interior of ∠𝐵𝐴𝐷.
ADJACENT ANGLES: Two angles ∠𝐵𝐴𝐶 and ∠𝐶𝐴𝐷 with a common side 𝐴𝐶
VERTICAL ANGLES: Two angles are vertical angles (or vertically opposite angles) if their sides form two pairs of opposite rays.
ANGLES ON A LINE: The sum of the measures of adjacent angles on a line is 180°.
ANGLES AT A POINT: The sum of the measures of adjacent angles at a point is 360°.
Exercise 5
The following figure shows four lines intersecting at a point. In a complete
sentence, describe the angle relationships in the diagram. Write an equation for
the angle relationship shown in the figure and solve for 𝑥 and 𝑦.
25°
x°
y°
40°
96°
Exercise 6
In a complete sentence, describe the angle relationships in the diagram. Write an
equation for the angle relationship shown in the figure and solve for 𝑥 and 𝑦.
27°
x°
y°
Exercise 7
In a complete sentence, describe the angle relationships in the diagram. Write an equation for
the angle relationship shown in the figure and solve for 𝑥. Find the measures of ∠𝐽𝐾𝐺.
J
L
G
24°
x°
5x° K
M
Lesson 7:
Angle Problems and Solving Equations
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M3-TE-1.3.0-08.2015
S.23
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 7
FUSD AZCCRS MATHEMATICS CURRICULUM
7•3
Example 5
In the accompanying diagram, the measure of ∠𝐷𝐵𝐸 is four times the
measure of ∠𝐹𝐵𝐺.
a. Label ∠𝐷𝐵𝐸 as 𝑦° and ∠𝐹𝐵𝐺 as 𝑥°. Write an equation that
describes the relationship between ∠𝐷𝐵𝐸 and ∠𝐹𝐵𝐺.
A
C
F
x°
B
50°
y°
D
G
b.
Find the value of 𝑥.
E
c.
Find the measures of ∠𝐹𝐵𝐺, ∠𝐶𝐵𝐷, ∠𝐴𝐵𝐹, ∠𝐺𝐵𝐸, and ∠𝐷𝐵𝐸.
d.
What is the measure of ∠𝐴𝐵𝐺? Identify the angle relationship used to get your answer.
Lesson 7:
Angle Problems and Solving Equations
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M3-TE-1.3.0-08.2015
S.24
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.