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Name
Class
Date
Lesson 6-1 Angle Measures
Lesson Objective
Common Core Standard
To write and solve equations to find
unknown angle measures
Geometry: 7.G.5
Vocabulary
An angle is a figure formed by two rays with a common endpoint.
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angle
between
0 ° and 90 °
right
obtuse angle
angle
between
90 ° and 180
90 °
straight
°
that share a vertex and a side
Adjacent angles are angles
180
°
Circle an angle
adjacent to 1.
but
have no interior points in common.
congruent angles formed by two
Vertical angles are the
4
intersecting
lines and are opposite each other.
1
3
2
2 or 4
Circle an vertical
angle to 1.
1
4
2
3
If the sum of the measure of two angles is 90°, the angles
are complementary . If the sum is 180°, the angles
are supplementary .
3
39 °
51°
angle
complementary
65°
115
°
supplementary
Congruent angles are angles with equal measures.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
acute
64
441197_C2_Ch6_WKbk_Ver-1.indd 64
Course 2 Lesson 6-1
Daily Notetaking Guide
10/10/12 2:20 PM
Name
Class
Date
Examples
1 Finding Supplements and Complements Write and solve an
equation to find the measures of the two angles described at the right.
6x 1 (19x 1 5) 5 180
1
d The angles are supplementary.
2
6x 1 19x 1 5 5 180
d Use the Associative Property.
25x 1 5 5 180
d Combine like terms.
19x 5°
6x
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25x 1 5 2 5 5 180 2 5 d Subtract 5 from each side.
25x 5 175 25x
25
5
175
25
x 5 7
d Simplify.
d Divide.
d Simplify.
Calculate the angle measures.
6 7  5
42 and 19  7  1 5 5 138
The angle measures are
42 ° and 138 °.
2 Finding Angle Measures In the diagram, m3 5 32°.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Find the measures of 1, 2, and 4.
m2 1 32° 5 180° d &2 and &3 are
1
supplementary .
2
4
3
m2 1 32° 2 32° 5 180° 2 32°d Subtract 32° from each side.
m2 5 148° d Simplify.
m1 5 32° d &1 and &3 are
vertical
angles.
m4 5 148° d &2 and &4 are
vertical
angles.
Quick Check
1. Write and solve an equation to find the measures of the two angles
described at the right. 65°; 115°
(13x)°
(11x 60)°
2. In the diagram at the right, m8 5 72°. Find the measures of
5, 6, and 7.
108°; 72°; 108°
Daily Notetaking Guide
441197_C2_Ch6_WKbk_Ver-1.indd 65
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5
7
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Course 2 Lesson 6-1
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10/10/12 2:20 PM