Triangle setup and solve

Problem:



Solution:

Let the first angle be $ a $, the second angle be $ b $ and the third angle $ c $.

The sum of the first and the second angle is twice of the third angle gives

$ a + b = 2c $ (Equation 1)

The measure of the second angle is 10 degree less than the third angle.

$ b = c - 10 $. (Equation 2)

Last but not least, they are angles in a triangle, so it satisfy $ a + b + c = 180 $. (Equation 3)

Next we solve these equations. Note that equation 2 is so simple, so we use it to substitute it in equation 1 and 3, gives

$ a + c - 10 = 2c $, which implies $ a - c = 10 $ (Equation 4) 
$ a + c - 10 + c = 180 $ which implies $ a + 2c = 190 $ (Equation 5)

Now, we use subtract equation 5 by equation 4, that gives

$ 3c = 180 $, then $ c = 60 $, the rest can be get easily

$ a = c + 10 = 70 $
$ b = c - 10 = 50 $