Angle Addition Postulate
First, let’s 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:
J
K
L
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…
Angle Addition Postulate
Slide 2
If B lies on the interior of AOC,
then mAOB + mBOC = mAOC.
B
A
mAOC = 115
50
O
65
C
Example 1:
D
Example 2:
G
114
K
95
19
H
Given: mGHK = 95
mGHJ = 114.
Find: mKHJ.
J
134°
A
Slide 3
46°
B
C
This is a special example, because the
two adjacent angles together create a
straight angle.
Predict what mABD + mDBC equals.
ABC is a straight angle, therefore
mABC = 180.
The Angle Addition Postulate
tells us:
mABD + mDBC = mABC
mGHK + mKHJ = mGHJ
95 + mKHJ = 114
mKHJ = 19.
Plug in what
you know.
Solve.
mABD + mDBC = 180
So, if mABD = 134,
46
then mDBC = ______
R
Given:
mRSV = x + 5
mVST = 3x - 9
mRST = 68
V
Find x.
S
T
Set up an equation using the Angle
Addition Postulate.
mRSV + mVST = mRST
x + 5 + 3x – 9 = 68
Solve.
4x- 4 = 68
4x = 72
x = 18
Plug in
what you
know.
Algebra Connection
Slide 4
Extension: Now that you
know x = 18, find mRSV
and mVST.
mRSV = x + 5
mRSV = 18 + 5 = 23
mVST = 3x - 9
mVST = 3(18) – 9 = 45
Check:
mRSV + mVST = mRST
23 + 45 = 68
B
C
mBQC = x – 7 mCQD = 2x – 1 mBQD = 2x + 34
Find x, mBQC, mCQD, mBQD.
mBQC = x – 7
mBQC = 42 – 7 = 35
Q
D
mBQC + mCQD = mBQD
x – 7 + 2x – 1 = 2x + 34
3x – 8 = 2x + 34
x – 8 = 34
x = 42
Algebra Connection
Slide 5
mCQD = 2x – 1
mCQD = 2(42) – 1 = 83
mBQD = 2x + 34
mBQD = 2(42) + 34 = 118
Check:
mBQC + mCQD = mBQD
35 + 83 = 118
x = 42
mCQD = 83
mBQC = 35 mBQD = 118