7•3
Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 11: Angle Problems and Solving Equations
Classwork
Opening Exercise
a.
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. Confirm your answers by measuring the angle with a
protractor.
14°
x°
b.
𝐶𝐷 and 𝐸𝐹 are intersecting lines. 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 𝑦. Confirm your answers by
measuring the angle with a protractor.
F
147°
C
D
51°
y°
E
Lesson 11:
Date:
Angle Problems and Solving Equations
2/9/16
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Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
c.
7•3
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 𝑏. Confirm your answers by measuring the angle with a
protractor.
59°
65°
41°
b°
d.
The following figure shows three lines intersecting at a point. 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 𝑧.
Confirm your answers by measuring the angle with a protractor.
z°
e.
158°
z°
Write an equation for the angle relationship shown in the figure and solve for 𝑥. In a complete sentence,
describe the angle relationship in the diagram. Find the measurements of ∠𝐸𝑃𝐵 and ∠𝐶𝑃𝐴. Confirm your
answers by measuring the angle with a protractor.
Lesson 11:
Date:
Angle Problems and Solving Equations
2/9/16
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Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
7•3
Example 1
The following figure shows three lines intersecting at a point. 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. Confirm your answers by
measuring the angle with a protractor.
68°
86°
x°
Exercise 1
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. Confirm your
answers by measuring the angle with a protractor.
25°
x°
y°
40°
96°
Example 2
In a complete sentence, describe the angle relationships in the diagram. You may label the diagram to help describe the
angle relationships. Write an equation for the angle relationship shown in the figure and solve for 𝑥. Confirm your
answers by measuring the angle with a protractor.
Lesson 11:
Date:
Angle Problems and Solving Equations
2/9/16
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7•3
Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
Exercise 2
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. Confirm your answers by measuring the angle with a protractor.
27°
x°
y°
Example 3
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 ∠𝐽𝐴𝐻 and ∠𝐺𝐴𝐹. Confirm your answers by measuring the
angle with a protractor.
H
J
2x°
G
3x°
225° A
F
Exercise 3
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 ∠𝐽𝐴𝐻 and ∠𝐺𝐴𝐹. Confirm your answers by measuring the
angle with a protractor.
J
L
G
24°
x°
5x° K
M
Lesson 11:
Date:
Angle Problems and Solving Equations
2/9/16
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Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
7•3
Example 4
In the accompanying diagram, ∠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 11:
Date:
Angle Problems and Solving Equations
2/9/16
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Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
7•3
Problem Set
In a complete sentence, describe the angle relationships in each diagram. Write an equation for the angle relationship(s)
shown in the figure, and solve for the indicated unknown angle. You can check your answers by measuring each angle
with a protractor.
1.
Find the measures of ∠𝐸𝐴𝐹, ∠𝐷𝐴𝐸, and ∠𝐶𝐴𝐷.
D
E
4x°
2x°
6x°
2.
30°
A
C
F
G
Find the measure of 𝑎.
126°
a°
a°
26°
3.
Find the measures of 𝑥 and 𝑦.
x°
25°
65°
y°
Lesson 11:
Date:
Angle Problems and Solving Equations
2/9/16
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Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
4.
7•3
Find the measure of ∠𝐻𝐴𝐽.
H
J
x°
E
81°
15°
A
F
G
5.
Find the measures of ∠𝐻𝐴𝐵 and ∠𝐶𝐴𝐵.
F
20°
A
E
D
H
3x°
2x°
C
6.
B
The measure of ∠𝑆𝑃𝑇 = 𝑏°. The measure of ∠𝑇𝑃𝑅 is five more than two times ∠𝑆𝑃𝑇. The measure of ∠𝑄𝑃𝑆 is
twelve less than eight times ∠𝑆𝑃𝑇. Find the measures of ∠𝑆𝑃𝑇, ∠𝑇𝑃𝑅, and ∠𝑄𝑃𝑆.
S
T
b°
(8b−12)°
Q
Lesson 11:
Date:
(2b+5)°
P
R
Angle Problems and Solving Equations
2/9/16
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Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
7.
7•3
Find the measures of ∠𝐻𝑄𝐸 and ∠𝐴𝑄𝐺.
E
H
C
2y°
21°
A
Q
B
y°
G
D
F
8.
The measures of three angles at a point are in the ratio of 2 ∶ 3 ∶ 5. Find the measures of the angles.
9.
The sum of the measures of two adjacent angles is 72°. The ratio of the smaller angle to the larger angle is 1 ∶ 3.
Find the measures of each angle.
10. Find the measures of ∠𝐶𝑄𝐴 and ∠𝐸𝑄𝐵.
B
E
4x°
F
18°
C
5x°
Q
D
A
Lesson 11:
Date:
Angle Problems and Solving Equations
2/9/16
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.