Algebra Word Problem 3

Let us call the angles F (first), S (second), and T (third).

It is given that the first angle is 1 degree more than twice the second, thus: F = 1 + 2S
Also, it is given that the third angle is 13 degrees less than the second, thus: T = S - 13.

Now, let us recall that the sum of all angles in a triangle is equal to 180 degres.

So F + S + T = 180. And substituting the equations above we have
(1 + 2S) + S + (S - 13) = 180
4S - 12 = 180
4S = 180 + 12
4S = 192
S = 192/4 = 48

Now,
F = 1 + 2S = 1 + 2 * 48 = 97
T = S - 13 = 48 - 13 = 35

The angles of this triangle are (in order, as written above) 97, 48 and 35.