SOLUTION: the measure of the largest angle of a triangle is 10 degrees more than the sum of the measures of two angles and 10 degrees less than 3 times the measure of the smallest angle. fin

Algebra ->  Rational-functions -> SOLUTION: the measure of the largest angle of a triangle is 10 degrees more than the sum of the measures of two angles and 10 degrees less than 3 times the measure of the smallest angle. fin      Log On


   

Question 1036917: the measure of the largest angle of a triangle is 10 degrees more than the sum of the measures of two angles and 10 degrees less than 3 times the measure of the smallest angle. find the measures of the three angles of the triangle
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
Three angles:
Small, Medium and Large
Make Small = x
10 degrees less than 3 times
the measure of the smallest angle.
Largest = 3x - 10.......(1)
0 degrees more than the sum of
the measures of two angles
Largest = 10 +(Small + Medium).....(2)
Largest = 10 + (x + Medium)
Medium = Largest -(10 + x)
Replace Largest with (3x - 10) from Eq(1)
Medium = 3x - 10 -(10 + x)
Medium = 3x - 20 - x
Medium = 2x - 20.
...........
Smallest = x
Medium = 2x - 20
Largest = 3x - 10
Add up:
x + 2x - 20 + 3x - 10 = 180
Collect like terms:
6x = 180 + 10 + 20
6x = 210
x = 35 degrees.
..........
Smallest = 35 degrees
Medium = 50 degrees
Largest = 95 degrees
Total = 180 degrees.
Hope this helps :-)