SOLUTION: The largest angle of a triangle is 6 times the smallest angle and it is 3 times the other angle. Find the size of the smallest angle. A. 40 degrees B. 30 degrees C. 20 degrees

Algebra ->  Triangles -> SOLUTION: The largest angle of a triangle is 6 times the smallest angle and it is 3 times the other angle. Find the size of the smallest angle. A. 40 degrees B. 30 degrees C. 20 degrees      Log On


   

Question 511010: The largest angle of a triangle is 6 times the smallest angle and it is 3 times the other angle. Find the size of the smallest angle.
A. 40 degrees
B. 30 degrees
C. 20 degrees
D. 10 degrees
So far I have tried all answers but they don't come to 180 degrees. My first thought was 30 degrees because then the other angle would be 90 but then that would require the largest angle to be 180. Now there is a 200 degree triangle but I am not sure if I am correct.
All help would be greatly appreciated!
Thank you,
Ann
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = the largest angle
Let B = the "other angle
let C = the smallest angle
:
Write an equation for each statement, get them all in terms of A:
:
"The largest angle of a triangle is 6 times the smallest angle"
A = 6C
Divide both sides by 6, and we have
C = 1%2F6A
:
and it is 3 times the other angle.
A = 3B
Divide both sides by 3
B = 1%2F3A
:
A + B + C = 180
therefore
A + 1%2F3A + 1%2F6A = 180
Get rid of those annoying fractions, multiply by 6 and we have
6A + 2A + A = 6(180)
9A = 1080
A = 1080%2F9
A = 120 degrees is the largest angle
:
Find the size of the smallest angle.
C = 1%2F6A
C = 1%2F6*120
C = 20 degrees
:
:
You can check this; find the other angle and ensure they add up to 180