SOLUTION: The second angle of a triangle garden is four times as large as the 1st. The third angle is 45 degree less than the sum o the other two angles. Find the measures of each angle. {{{

Algebra ->  Graphs -> SOLUTION: The second angle of a triangle garden is four times as large as the 1st. The third angle is 45 degree less than the sum o the other two angles. Find the measures of each angle. {{{      Log On


   

Question 976150: The second angle of a triangle garden is four times as large as the 1st. The third angle is 45 degree less than the sum o the other two angles. Find the measures of each angle. +Please+help+me+solve+this+problem
x+4x + (5x-45)=180
x+4x + (5x-45) = 10-45
10x + 45-45 = 180 -45
10x = 135
10/10 = 135/10
x = 13.5 ?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
first angles x and y; last angle z.

system%28y=4x%2Cz=-45%2Bx%2By%2Cx%2By%2Bz=180%29

More than one way to go.

z=x%2B4x-45
z=5x-45

x%2B%284x%29%2Bz=180
x%2B4x%2B%285x-45%29=180
5x%2B5x-45=180
10x-45=180
10x=180%2B45
10x=225
highlight%28x=22.5%29---------you can now find the other angles, y and z.


----
Another way:
Put the system into x,y,z form.
system%284x-y%2B0%2Az=0%2Cx%2By-z=45%2Cx%2By%2Bz=180%29

system%28x%2By%2Bz=180%2Cx%2By-z=45%2C4x-y%2B0%2Az=0%29
R2=R2-R1, R3=R3-4*R1

system%28x%2By%2Bz=180%2C-2z=45-180%2C0%2Ax-y-4%2Ay%2B0%2Az-4z=0-4%2A180%29

system%28x%2By%2Bz=180%2C-2z=-135%2C0%2Ax-5y-4z=-720%29

Look at last two equations.
system%28z=135%2F2%2C5y%2B4z=720%29
-
5y=720-4z
y=%28720-4z%29%2F5
y=%28720-4%28135%2F2%29%29%2F5
y=%28720-270%29%2F5
highlight%28y=90%29------and you already have the value of z...
-
z=135%2F2
or
highlight%28z=67%261%2F2%29
-
Use z and y to find value for x.
x=180-y-z
x=180-90-135%2F2
x=180-90-67%261%2F2
x=90-67%261%2F2
highlight%28x=22%261%2F2%29