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8-3 Angle Relationships8-3 Angle Relationships
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
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8-3 Angle Relationships
Warm UpIdentify the type of angle.
1. 70°
2. 90°
3. 140°
4. 180°
acute
right
obtuse
straight
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Course 1
8-3 Angle Relationships
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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Course 1
8-3 Angle Relationships
Learn to understand relationships of angles.
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8-3 Angle Relationships
Vocabulary
congruentvertical anglesadjacent anglescomplementary anglessupplementary angles
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8-3 Angle Relationships
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.
MRP and NRQ are vertical angles.
MRN and PRQ are vertical angles
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8-3 Angle Relationships
Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent.
MRN and NRQ are adjacent angles. They share vertex R and RN.
NRQ and QRP are adjacent angles. They share vertex R and RQ.
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8-3 Angle Relationships
Additional Example 1A: Identifying Types of Angle Pairs
Identify the type of each angle pair shown.
5 and 6 are opposite each other and are formed by two intersecting lines.
They are vertical angles.
5 6
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8-3 Angle Relationships
Additional Example 1B: Identifying Types of Angle Pairs
Identify the type of each angle pair shown.
7 and 8 are side by side and have a common vertex and ray.
They are adjacent angles.
7 8
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8-3 Angle Relationships
Check It Out: Example 1A
Identify the type of each angle pair shown.
3 and 4 are side by side and have a common vertex and ray.
They are adjacent angles.
3
4
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8-3 Angle Relationships
Check It Out: Example 1B
Identify the type of each angle pair shown.
7 and 8 are opposite each other and are formed by two intersecting lines.
They are vertical angles.
7
8
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8-3 Angle Relationships
65° + 25° = 90°
LMN and NMP are complementary.
Complementary angles are two angles whose measures have a sum of 90°.
P
N
M
L
25°65°
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8-3 Angle Relationships
Supplementary angles are two angles whose measures have a sum of 180°.
65° + 115° = 180°
GHK and KHJ are supplementary.
J
K
H
115°65°
G
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8-3 Angle Relationships
Additional Example 2A: Identifying an Unknown Angle Measure
Find each unknown angle measure.
71° + 1 = 90°–71° –71°
m1 = 19°
The sum of the measures is 90°.
1
71°
The angles are complementary.
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8-3 Angle Relationships
Additional Example 2B: Identifying an Unknown Angle Measure
Find each unknown angle measure.
125° + 2 = 180°–125° –125°
m2 = 55°
The sum of the measures is 180°.
2125°
The angles are supplementary.
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8-3 Angle Relationships
Additional Example 2C: Identifying an Unknown Angle Measure
Find each unknown angle measure.
m3 = 82° Vertical angles are congruent.
3 82°
The angles are vertical angles.
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8-3 Angle Relationships
Additional Example 2D: Identifying an Unknown Angle Measure
Find each unknown angle measure.
x + y + 80° = 180°–80° –80°
x + y = 100°
The sum of the measures is 180°.
JKL and MKN are congruent.
x = 50° and y = 50° Each angle measures half of 100°.
x 80°
K
ML
NJ
y
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8-3 Angle Relationships
Check It Out: Example 2A
Find each unknown angle measure.
65° + d = 90°–65° –65°
md = 25°
The sum of the measures is 90°.
d
65°
The angles are complementary.
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8-3 Angle Relationships
Check It Out: Example 2B
Find each unknown angle measure.
145° + s = 180°–145° –145°
ms = 35°
The sum of the measures is 180°.
s145°
The angles are supplementary.
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8-3 Angle Relationships
Check It Out: Example 2C
Find each unknown angle measure.
mt = 32° Vertical angles are congruent.
t
32°
The angles are vertical angles.
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8-3 Angle Relationships
Check It Out: Example 2D
Find each unknown angle measure.
x + y + 50° = 180°–50° –50°
x + y = 130°
The sum of the measures is 180°.
ABC and DBE are congruent.
x = 65° and y = 65° Each angle measures half of 130°.
x50°
B
DC
EA
y
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Course 1
8-3 Angle Relationships
Lesson Quiz
1. Identify the type of angle pair shown.
Find each unknown angle measure.
2. The angles are vertical angles.
3. The angles are supplementary.
adjacent
d = 130°
67
x = 45°
d
130°
x 135°