The sum of the measures of the angles of a triangle is 180. the sum of the measures of the second and third angles is twice the measure of the first angle. the third angle is 12 more than the second.

let x, y, and z represent the measures of the first, second, and third angles, respectively. find the measures of the three angles.

x = first angle

y = second angle

z = third angle

x + y + z = 180

The sum of the measures of the second and third angles is twice the measure of the first angle.    >       y + z = 2x

The third angle is 12 more than the second.  >    z = y + 12

Use substitution to find each variable. Since z is already isolated/by itself, plug it into the other equation

y + z = 2x    Plug in (y + 12) for z

y + (y + 12) = 2x      Simplify

2y + 12 = 2x    Divide 2 on both sides

y + 6 = x          Isolate "y"

y = x - 6         Next you could plug this into z = y + 12, so that z has the x variable

z = y + 12

z = x - 6 + 12

z = x + 6

Now that you have y and z, you can do this:

x + y + z = 180

x + (x - 6) + (x + 6) = 180     Simplify

3x = 180    Divide 3 on both sides

x = 60             Now that you found x, plug it into the other equations to find y and z

y = x - 6

y = 60 - 6

y = 54

z = x + 6

z = 60 + 6

z = 66

x = 60°

y = 54°

z = 66°          [sorry if this is confusing]

PROOF

x + y + z = 180

60 + 54 + 66 = 180

180 = 180