Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
7•6
Lesson 4: Solving for Unknown Angles Using Equations
Classwork
Opening Exercise
Four times the measurement of an angle is the complement of the angle. Find the measurement of the angle and its
complement.
Example 1
Find the measurement of ∠𝐹𝐴𝐸 and ∠𝐶𝐴𝐷.
Two lines meet at a point. List the relevant angle relationship in the diagram. Set up and solve an equation to find the
value of 𝑥. Find the measurement of one of the vertical angles.
(x+64)°
3x°
Lesson 4:
Date:
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Solving Unknown Angles Using Equations
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Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
7•6
Exercise 1
Set up and solve an equation to find the value of 𝑥. List the relevant angle relationship in the diagram. Find the
measurement of one of the vertical angles.
5x°
(x+132)°
Example 2
Three lines meet at a point. List the relevant angle relationships in the diagram. Set up and solve an equation to find the
value of 𝑏.
b°
43°
37°
Exercise 2
Two lines meet at the common vertex of two rays. List the relevant angle relationships in the diagram. Set up and solve
an equation to find the value of 𝑏.
95°
b°
Lesson 4:
Date:
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80°
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Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
7•6
Example 3
2
The measurement of an angle is the measurement of its supplement. Find the measurement of the angle.
3
Exercise 3
1
The measurement of an angle is the measurement of its complement. Find the measurement of the angle.
4
Example 4
Three lines meet at the common vertex of a ray. List the relevant angle relationships in the diagram. Set up
and solve an equation to find the value of 𝒛.
29°
z°
Lesson 4:
Date:
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Solving Unknown Angles Using Equations
2/6/16
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Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
7•6
Exercise 4
Two lines meet at the common vertex of two rays. Set up and solve an equation to find the value of 𝒙. Find
the measurement of ∠𝑮𝑨𝑭 and of ∠𝑩𝑨𝑪.
F
G
E
4x°
36°
C
5x°
A
D
B
Lesson 4:
Date:
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Solving Unknown Angles Using Equations
2/6/16
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7•6
Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
Problem Set
1.
Four rays have a common vertex on a line. Set up and solve an equation to
find the value of 𝑐.
c°
d°
140°
59°
2.
Lines ⃡𝐵𝐶 and ⃡𝐸𝐹 meet at 𝐴. Set up and solve an equation to find the value of 𝑥.
Find the measurements of ∠𝐸𝐴𝐻 and ∠𝐻𝐴𝐶.
E
B
3x°
57°
A
D
4x°
C
F
3.
G
Five rays meet at a point. Set up and solve an equation to find the values of
𝑥. Find the measurements of ∠𝐷𝐴𝐺 and ∠𝐺𝐴𝐻.
2x°
3x°
A
D
36.5°
E
4.
H
2x°
H
36.5°
F
Two perpendicular lines meet at the common vertex of seven rays. Set up
and solve an equation to find the values of 𝑥 and 𝑦.
15°
x°
x°
y°
y°
x°
12°
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Date:
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5.
7•6
Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
Two lines meet at the common vertex of two perpendicular rays. Set up and solve
an equation to find the value of 𝑥. Find the measurements of ∠𝐶𝐴𝐸 and ∠𝐵𝐴𝐺.
C
A
D
15°
4x°
E
F
3x°
B
G
6.
Three angles are at a point. The second angle is 20° more than the first, and the third angle is 20° more than the
second. Find the measurements of all three angles.
7.
Five angles are at a point. The measurement of each angle is one of five consecutive, positive whole numbers.
8.
a.
Determine the measurements of all five angles.
b.
Compare the expressions you used for the three angles and their combined expression. Explain how they are
equivalent and how they reveal different information about this situation.
Let 𝑥° be the measurement of an angle. The ratio of the measurement of the complement of the angle to the
1
measurement of the supplement of the angle is . Use a tape diagram to find the measurement of this angle.
3
9.
Two lines meet at a point. Set up and solve an equation to find the value of 𝑥. Find the measurement of one of the
vertical angles.
(x+117)°
4x°
10. The difference between three times the measurement of the complement of an angle and the measurement of the
supplement of that angle is 20°. What is the measurement of the angle?
Lesson 4:
Date:
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