Activity
7.1
Start Thinking!
For use before Activity 7.1
What is an acute angle?
What is an obtuse angle?
Use a dictionary to look up the non-math
definitions of acute and obtuse. How do the
definitions relate to the math definitions?
Activity
7.1
Warm Up
For use before Activity 7.1
Identify the angles as acute, right, obtuse, or
straight.
1.
2.
3.
4.
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Lesson
7.1
Start Thinking!
For use before Lesson 7.1
Draw two lines that intersect. Explain to a
partner how to locate a pair of adjacent angles.
Lesson
7.1
Warm Up
For use before Lesson 7.1
Use the figure below.
A
E
B
C
D
1. Measure each angle formed by the
intersecting lines.
2. Name two angles that are adjacent to ∠ ABC .
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Name_________________________________________________________
7.1
Date __________
Practice A
Name two pairs of adjacent angles and two pairs of vertical angles in
the figure.
1.
2.
C
B
A
I
G
D
H
E
N
J
M
L
K
Tell whether the angles are adjacent or vertical. Then find the value of x.
3.
x°
4.
142°
x°
6.
6x°
32°
5.
(x − 2)°
3x°
2x°
Draw a pair of vertical angles with the given measure.
7. 40°
8. 75°
9. 120°
10. Draw a pair of adjacent angles with the given description.
a. Both angles are obtuse.
b. The sum of the angle measures is 180°.
c. The sum of the angles measures is 60°.
11. What are the measures of the
other three angles formed by
the intersection?
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1
132°
2
3
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Name _________________________________________________________ Date _________
5.1
7.1
Practice B
Name two pairs of adjacent angles and two pairs of vertical angles in
the figure.
1.
2.
F
V
T
W
E
D
G
I
U
S
Z
H
X
Y
Tell whether the angles are adjacent or vertical. Then find the value of x.
3.
4.
x° 57°
x°
80°
5.
6.
4x°
3x° x°
(5x − 30)°
Draw a pair of vertical angles with the given measure.
7. 100°
8. 15°
9. 150°
10. Draw five angles so that ∠2 and ∠3 are acute vertical angles, ∠1 and ∠2
are supplementary, ∠2 and ∠5 are complementary, and ∠4 and ∠5 are
adjacent.
11. The measures of two adjacent angles have a ratio of 3 : 5. The sum of the
measures of the two adjacent angles is 120°. What is the measure of the
larger angle?
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7.1
Date __________
Enrichment and Extension
Compass Straightedge Construction
In addition to modern technology, a geometer’s most important tools are a
compass and a straightedge (ruler without marks). These instruments can
be used for geometric drawings called constructions.
Bisecting the Angle
Bisecting the angle is the process of cutting a given angle in half so that both
halves are equal. This can be done using only a compass and straightedge.
A
1. Classify angle A.
2. Open the compass. Place the point of the compass at A and draw an arc
(a small curved line that is part of a circle) that intersects both sides of
the angle. Label the points where the curved line intersects the angle as
B and C.
3. Place the point of the compass on B. Draw an arc that is contained within
the angle. Without changing the width of the compass, place the point
of the compass on C and draw an arc that intersects the one just drawn.
4. Label the intersection point of the two arcs G. Use a straightedge to
connect points A and G. The line segment AG bisects angle BAC.
5. Use a protractor to measure angle BAC. Divide this measure by two to
determine what each smaller angle should measure. Then, use your
protractor and measure the smaller angles. How do the numbers compare?
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Name _________________________________________________________ Date _________
7.1 Puzzle Time
What Runs Around All Day And Lies Under The Bed With Its
Tongue Hanging Out?
Write the letter of each answer in the box containing the exercise number.
Tell whether the angles are adjacent or vertical.
1.
2.
Answers
3x°
N. 29
(2x + 50)°
120° x°
K. vertical
3.
A. 160
80°
S. 60
(4x − 140)°
E. adjacent
R. 135
E. adjacent
Find the value of x.
4.
A. 110
5.
x°
x°
151°
110°
6.
7.
x°
30°
20°
x°
8. A road intersects another road
at an angle of 45°. Find the
value of x.
7
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x° 45°
6
5
3
4
2
1
8
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