SOLUTION: I'm hopeless ! In a triangle, the largest angle is 100 degrees greater than the smallest angle. The largest angle is three times as large as the third angle. What is the measure

Algebra ->  Linear-equations -> SOLUTION: I'm hopeless ! In a triangle, the largest angle is 100 degrees greater than the smallest angle. The largest angle is three times as large as the third angle. What is the measure      Log On


   

Question 267902: I'm hopeless !
In a triangle, the largest angle is 100 degrees greater than the smallest angle. The largest angle is three times as large as the third angle. What is the measure of each angle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I don't think you are hopeless at all, how about a step-by-step method here?
Let x = the largest angle
:
"the largest angle is 100 degrees greater than the smallest angle."
(x-100) = the smallest angle
:
"The largest angle is three times as large as the third angle."
1%2F3x = the 3rd angle
:
Now we have an expression for all 3 angles using x
:
What is the measure of each angle?
I'm sure you know that a triangle has a total of 180 degrees
:
Large + small + 3rd angle = 180
x + (x-100) + 1%2F3x = 180
2x + 1%2F3x - 100 = 180
2x + 1%2F3x = 180 + 100
2x + 1%2F3x = 280
Multiply by 3 to get rid of the denominator, results
3(2x) + x = 3(280)
:
6x + x = 840
;
7x = 840
x = 840%2F7
x = 120 degrees is the largest angle
then
1%2F3 * 120 = 40 degrees is the 3rd angle
and
120 - 100 = 20 degrees is the smallest angle
:
;
Check our answers
120 + 40 + 20 = 180 degrees
:
:
Hope this relieves you of that hopeless feeling!!
If you have any questions about this, you can email me. ankor@att.net