SOLUTION: In the diagram of triangle ABC, side BC is extended to D [IMG]C:\Users\user\Pictures\p16a.gif[/IMG] If m<A= x^2-6x , m<B= 2x-3, and m<ACD= 9x+27, what is the value of x?

Algebra ->  Triangles -> SOLUTION: In the diagram of triangle ABC, side BC is extended to D [IMG]C:\Users\user\Pictures\p16a.gif[/IMG] If m<A= x^2-6x , m<B= 2x-3, and m<ACD= 9x+27, what is the value of x?      Log On


   

Question 733053: In the diagram of triangle ABC, side BC is extended to D
[IMG]C:\Users\user\Pictures\p16a.gif[/IMG]
If m
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If
m< A=+x%5E2-6x ,
m< B=+2x-3, and
m< ACD=+9x%2B27,
what is the value of x?
recall:
The exterior angle theorem: the exterior angle of a triangle is equal to the sum of the two remote interior angles
so, m< ACD=m< A+ m< B
then you have
9x%2B27=x%5E2-6x%2B2x-3
9x%2B27=x%5E2-4x-3
x%5E2-4x-9x-3-27=0
x%5E2-13x-30=0...factor...replace -13x with -15x%2B2x
x%5E2-15x%2B2x-30=0
%28x%5E2-15x%29%2B%282x-30%29=0
x%28x-15%29%2B2%28x-15%29=0
%28x%2B2%29%28x-15%29=0
so, if x%2B2=0...=>...x=-2....this solution make equation true, but it could not work with angle measure because it cannot be negative
if x-15=0...=>...x=15...so, your solution is:
highlight%28x+=+15%29+
now find the measure of each angle:
m< A=+15%5E2-6%2A15...=>A=+225-90..=>A=+135
m< B=+2%2A15-3...=> B=30-3..=> B=27
m< ACD=+9%2A15%2B27...=>ACD=+135%2B27..=>ACD=+162