Respuesta :
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
