Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Identify the type of angle. 1. 70 2.
90 3. 140 4. 180
acute
right
obtuse
straight
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Problem of the Day A line forms an angle of 57
with the vertical axis. What angle does the line
form with the horizontal axis?
33 or 147
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Learn to understand relationships of angles.
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Insert Lesson Title Here
Vocabulary
congruent vertical angles adjacent
angles complementary angles supplementary angles
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When angles have the same measure, they are said
to be congruent.
Vertical angles are formed opposite each other
when two lines intersect. Vertical angles have
the same measure, so they are always congruent.
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Adjacent angles are side by side and have a
common vertex and ray. Adjacent angles may or may
not be congruent.
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Additional Example 1A Identifying Types of Angle
Pairs Identify the type of each angle pair
shown. A.
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They are vertical angles.
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Additional Example 1B Identifying Types of Angle
Pairs Identify the type of each angle pair
shown. B.
7 8
They are adjacent angles.
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Try This Additional Example 1A Identify the type
of each angle pair shown. A.
3
4
They are adjacent angles.
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Try This Additional Example 1B Identify the type
of each angle pair shown. B.
7
8
They are vertical angles.
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Complementary angles are two angles whose
measures have a sum of 90.
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Supplementary angles are two angles whose
measures have a sum of 180.
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Additional Example 2A Identifying an Unknown
Angle Measure Find each unknown angle measure.
A. The angles are complementary.
The sum of the measures is 90.
71 a 90
a
71 71
a 19
71
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Additional Example 2B Identifying an Unknown
Angle Measure Find each unknown angle measure.
B. The angles are supplementary.
125 b 180
The sum of the measures is 180.
125 125
b 55
125
b
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Additional Example 2C Identifying an Unknown
Angle Measure Find each unknown angle measure.
C. The angles are vertical angles.
c
82
c 82
Vertical angles are congruent.
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Additional Example 2D Identifying an Unknown
Angle Measure Find each unknown angle measure.
D. JKL and MKN are congruent.
x y 80 180
The sum of the measures is 180.
80 80
x y 100
Each angle measures half of 100.
x 50 and y 50
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Try This Example 2A Find each unknown angle
measure.
A. The angles are complementary.
65 d 90
The sum of the measures is 90.
d
65 65
d 25
65
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Try This Example 2B Find each unknown angle
measure.
B. The angles are supplementary.
145 s 180
The sum of the measures is 180.
145 145
s 35
145
s
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Try This Example 2C Find each unknown angle
measure.
C. The angles are vertical angles.
t
t 32
Vertical angles are congruent.
32
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Try This Example 2D Find each unknown angle
measure.
D. ABC and DBE are congruent.
x y 50 180
The sum of the measures is 180.
50 50
x y 130
Each angle measures half of 130.
x 65 and y 65
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Insert Lesson Title Here
Lesson Quiz
Give the complement of each angle. 1. 70 2.
42 Give the supplement of each angle. 3. 120
4. 17 5. Identify the type of angle pair
shown.
48
20
60
163
adjacent