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

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) (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.
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