The angle additional postulate tells us that
m∠ABC = m∠ABD + m∠DBC
Substituing in the values given,
10x - 7 = ( 6x+5) + (36)
NOTE: I have left off the degree marks purely for simplicity during the next few steps.
10x - 7 = 6x + ( 5 + 36 )
Application of the associative law of addition.
10x - 7 = 6x + 41
Add 7 to both sides:
10x = 6x + 41 + 7 = 6x + 48
Subtract 6x from both sides so that all the variables are on one side of the equation, and all the constants are on the other side.
4x = 48
If you have 10 apples and you eat 6, you have 4 left.
We don't care what 4x is. We want to know what x (1x) is. So divide both sides by 4.
x = 12
Are we done? Nope. The problem asks for the measure of ∠ABD.
6x + 5 = 6×12 + 5 = 72 + 5 = 77
The units are degrees, so our final answer is 77º
Are we there yet? Nope!
We always need to check our work.
Use the equations at the top.
m∠ABC = 10x-7 = 10×12 -7 = 120 -7 =113
Do our calculated values solve the problem?
m∠ABC ?= m∠ABD + ∠DBC
Substituting in our values,
113 = 77 + 36 = 113
Which verifies our answer. We are now done.
Note: once again, I left off the degree marks, purely for simplicity during this verification process.
