Question

The sum of the angle measures of any triangle is 180 degrees. find the angle measures of a triangle if the second angle measures twice the first, and the third angle measures 15 degrees less than the second.

Answer 1

a+b+c= 180
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 = 85Check by adding them up.
35 + 60 + 85 = 180
Done.