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Section 1.6 Geometry

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on 17 October 2013

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Transcript of Section 1.6 Geometry

Section 1.6
Angle Pair Relationships

Definitions
Vertical Angles
Linear Pairs
Example 2
Example 3
Example 1
Definitions
Vertical Angles- Two angles with sides that form two pairs of opposite rays
Linear Pair- Two adjacent angles with noncommon sides that form opposite rays
Vertical Angles are congruent, so:
<1 is congruent to <3

<2 is congruent to <4
Name: <MNP and <PNO
The m<3 = 55°
2c+4=6c-12
2c+4+12=6c-12+12
2c+16=6c
2c-2c=16=6c-2c
16=4c
16/4=4c/4
c=4
m<2=81° (180°-99°)
1
2
3
4
and
M
N
O
P
45°
135°
Sum of the angle measures is always 180°
2
55°
1
4
Find the measures of the missing angles
m<1= 125° (180°-55°)
m<2= 55° (Vertical Angles)
m<4= 125° (180°-55°)
Solve for C and find the missing angles.
(2c+4)°
(6c-12)°
2(4)+4=12°
6(4)-12=12°
99°
2
The measure of angle 1 is 99°, find the measure of angle 2.
Complementary: Two angles with a sum of 90°
Supplementary: Two angles with a sum of 180°
Example 4
<C and <M are Complementary. If m<M=65°, find m<C.
M
C
m<C=25° (90°-65°)
Example 5
Find the values of the variables
135°
(2r+35)°
1
2
3
4
s °

2r+35=135
2r+35-35=135-35
2r=100
2r/2=100/2
r=50°
**The angles are considered to be adjacent if they are directly touching each other. Supplementary and Complementary angles can either be adjacent or nonadjacent.
s+50=180
s+50-50=180-50
s=130°
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