SOLUTION: (3x-2), (2x+3), and (x+8) equal 180 degrees in a triangle. What is x?

Algebra ->  Triangles -> SOLUTION: (3x-2), (2x+3), and (x+8) equal 180 degrees in a triangle. What is x?      Log On


   

Question 661933: (3x-2), (2x+3), and (x+8) equal 180 degrees in a triangle. What is x?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
alpha=%283x-2%29, beta=%282x%2B3%29, and gamma=%28x%2B8%29

%283x-2%29%2B%282x%2B3%29%2B%28x%2B8%29=180+

3x-2%2B2x%2B3%2Bx%2B8=180+

6x%2B9=180+
6x=180+-9

6x=171

x=171%2F6

highlight%28x=28.5%29

alpha=3x-2,

alpha=3%2A28.5-2
alpha=85.5-2

alpha=83.5


beta=2x%2B3,
beta=2%2A28.5%2B3
beta=57%2B3
beta=60

and
gamma=x%2B8
gamma=28.5%2B8
gamma=36.5

check:

alpha%2Bbeta%2Bgamma=180
83.5%2B60%2B36.5=180
180=180