Angle Addition Postulate

1
Angle Addition Postulate
First, lets recall some previous information
from last week. We discussed the Segment
Addition Postulate, which stated that we could
add the lengths of adjacent segments together to
get the length of an entire segment. For
example JK KL JL If you know
that JK 7 and KL 4, then you can conclude
that JL 11. The Angle Addition Postulate is
very similar, yet applies to angles. It allows
us to add the measures of adjacent angles
together to find the measure of a bigger angle
2
Angle Addition Postulate
Slide 2
If B lies on the interior of ÐAOC, then mÐAOB
mÐBOC mÐAOC.
B
A
mÐAOC 115
C
O
3
Example 1
Example 2
Slide 3
G
K
46
19
This is a special example, because the two
adjacent angles together create a straight angle.
Predict what mÐABD mÐDBC equals. ÐABC is
a straight angle, therefore mÐABC 180. mÐABD
mÐDBC mÐABC mÐABD mÐDBC 180 So, if
mÐABD 134, then mÐDBC ______
H
J
Given mÐGHK 95 mÐGHJ 114. Find
mÐKHJ. The Angle Addition Postulate tells
us mÐGHK mÐKHJ mÐGHJ 95 mÐKHJ
114 mÐKHJ 19.
Plug in what you know.
46
Solve.
4
Algebra Connection Slide 4
Given mÐRSV x 5 mÐVST 3x - 9 mÐRST 68
Find x.
R
V
Extension Now that you know x 18, find mÐRSV
and mÐVST. mÐRSV x 5 mÐRSV 18 5
23 mÐVST 3x - 9 mÐVST 3(18) 9
45 Check mÐRSV mÐVST mÐRST 23 45 68
S
T
Set up an equation using the Angle Addition
Postulate.
mÐRSV mÐVST mÐRST x 5 3x 9 68 4x- 4
68 4x 72 x 18
Plug in what you know.
Solve.
5
mÐBQC x 7 mÐCQD 2x 1 mÐBQD 2x
34 Find x, mÐBQC, mÐCQD, mÐBQD.
C
B
mÐBQC x 7 mÐBQC 42 7 35 mÐCQD 2x
1 mÐCQD 2(42) 1 83 mÐBQD 2x 34 mÐBQD
2(42) 34 118 Check mÐBQC mÐCQD mÐBQD 35
83 118
Q
D
mÐBQC mÐCQD mÐBQD
x 7 2x 1 2x 34
3x 8 2x 34
x 8 34
x 42
Algebra Connection Slide 5