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

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