SOLUTION: The sum of the measures of any triangle is 180 degrees. Find the angle measures of a triangl if the second angle measures 10 degerees less than twice the first, and the third angle

Algebra ->  Equations -> SOLUTION: The sum of the measures of any triangle is 180 degrees. Find the angle measures of a triangl if the second angle measures 10 degerees less than twice the first, and the third angle      Log On


   

Question 248489: The sum of the measures of any triangle is 180 degrees. Find the angle measures of a triangl if the second angle measures 10 degerees less than twice the first, and the third angle measures 25 degrees more than the second.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
You have 3 angles: a, b & c.
a + b + c = 180
.
To define the equations, you can just start with a.
a = ?
.
b = 2a - 10 (twice a minus 10)
.
c = b + 25 (25 more than b)
.
Substitute for b
c = (2a-10) + 25
.
Now substitute back into a+b+c=180
a + (2a-10) + (2a-10+25) = 180
.
Eliminate the parentheses
a + 2a - 10 + 2a - 10 + 25 = 180
.
Combine like terms
5a + 5 = 180
.
Subtract 5 from both sides
5a = 175
.
Divide both sides by 5
a = 35
.
Substitute into the equation for b.
b = 2a -10 = 2*35 - 10 = 70 - 10 = 60
.
Add 25 to b to get c.
c = 60 + 25 = 85
.
Check by adding them up.
35 + 60 + 85 = 180
Done.