1. 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:
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… J K L

2. Angle Addition Postulate
Slide 2
If B lies on the interior of ÐAOC,
then mÐAOB + mÐBOC = mÐAOC. B A
mÐAOC = 115°
50°
65° C O

3. A B C D G K H J 134° 46° 46 Given: mÐGHK = 95 mÐGHJ = 114.
Example 1:
Example 2:
Slide 3 G
114° K
46°
95°
19° H
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 = ______ 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. Set up an equation using the Angle Addition Postulate.
Given:
mÐRSV = x + 5
mÐVST = 3x - 9
mÐRST = 68
Find x.
Algebra Connection
Slide 4 R V
Extension: Now that you know x = 18, find mÐRSV and mÐVST.
mÐRSV = x + 5
mÐRSV = = 23
mÐVST = 3x - 9
mÐVST = 3(18) – 9 = 45
Check:
mÐRSV + mÐVST = mÐRST
= 68 S T
Set up an equation using the Angle Addition Postulate.
mÐRSV + mÐVST = mÐRST
x x – 9 = 68
4x- 4 = 68
4x = 72
x = 18
Plug in what you know.
Solve.

5. x – 7 + 2x – 1 = 2x + 34 3x – 8 = 2x + 34 x – 8 = 34 x = 42 x = 42 C B
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
= 118 Q D
mÐBQC + mÐCQD = mÐBQD
x – 7 + 2x – 1 = 2x + 34
3x – 8 = 2x + 34
x – 8 = 34
x = 42
x = 42
mÐBQC = 35
mÐCQD = 83
mÐBQD = 118
Algebra Connection
Slide 5