1. 8-3 Angle Relationships
8-3 Angle Relationships
Warm Up
Problem of the Day
Lesson Presentation
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Course

2. 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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3. 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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4. 8-3 Angle Relationships
Additional Example 1A: Identifying Types of
Angle Pairs
Identify the type of each angle pair shown.
5 6
5 and 6 are opposite each other and
are formed by two intersecting lines.
They are vertical angles.
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5. 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
7 ray.
8
They are adjacent angles.
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6. 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.
3
4
They are adjacent angles.
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7. 8-3 Angle Relationships
Check It Out: Example 1B
Identify the type of each angle pair shown.
7
8
7 and 8 are opposite each other and
are formed by two intersecting lines.
They are vertical angles.
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8. 8-3 Angle Relationships
Complementary angles are two angles
whose measures have a sum of 90 .
65 + 25 = 90
LMN and NMP are complementary.
L
N
65
25
M P
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9. 8-3 Angle Relationships
Supplementary angles are two angles whose
measures have a sum of 180 .
65 + 115 = 180
GHK and KHJ are supplementary.
K
65 115°
G H J
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10. 8-3 Angle Relationships
Additional Example 2A: Identifying an
Unknown Angle Measure
Find each unknown angle measure.
The angles are complementary.
71 + 1= 90 The sum of
–71 –71 the measures 1
is 90 .
m 1= 19 71
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11. 8-3 Angle Relationships
Additional Example 2B: Identifying an
Unknown Angle Measure
Find each unknown angle measure.
The angles are supplementary.
125 + 2 = 180 The sum of
–125 –125 the measures
is 180 .
m 2= 55
125 2
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12. 8-3 Angle Relationships
Additional Example 2C: Identifying an
Unknown Angle Measure
Find each unknown angle measure.
The angles are vertical angles.
m 3 = 82 Vertical angles 3 82
are congruent.
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13. 8-3 Angle Relationships
Additional Example 2D: Identifying an
Unknown Angle Measure
Find each unknown angle measure.
JKL and MKN are M
L
congruent.
80
x y
J K N
x + y + 80 = 180 The sum of the measures is
–80 –80 180 .
x + y = 100
x = 50 and y = 50 Each angle measures half of
100 .
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14. 8-3 Angle Relationships
Check It Out: Example 2A
Find each unknown angle measure.
The angles are complementary.
65 + d = 90 The sum of
–65 –65 the measures d
m d = 25 is 90 . 65
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15. 8-3 Angle Relationships
Check It Out: Example 2B
Find each unknown angle measure.
The angles are supplementary.
145 + s = 180 The sum of the
–145 –145 measures is 180 .
m s= 35
145 s
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16. 8-3 Angle Relationships
Check It Out: Example 2C
Find each unknown angle measure.
The angles are vertical angles.
t
m t = 32 Vertical angles 32
are congruent.
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17. 8-3 Angle Relationships
Check It Out: Example 2D
Find each unknown angle measure.
ABC and DBE are C D
congruent. 50
x y
A B E
x + y + 50 = 180 The sum of the measures is
–50 –50 180 .
x + y = 130
x = 65 and y = 65 Each angle measures half of
130 .
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18. 8-3 Angle Relationships
Lesson Quiz
1. Identify the type of angle
pair shown. 6
adjacent 7
Find each unknown angle measure.
2. The angles are vertical angles. d
d = 130°
130
3. The angles are supplementary.
x = 45°
x 135
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