The total measures of the angles of a triangle equals 180 degrees.

We will call the three angles we have x, y, and z. So we have:

x + y + z = 180

And

x:y:z = 3:3:4

From this, I can conclude that:

y/x = 3/3 --> 3y = 3x --> y = x

z/x = 4/3 --> 3z = 4x --> z = 4/3*x

Plugging these into the sum of the angles above, we get:

x + x + 4/3*x = 180

10/3*x = 180

x = 54 degrees

y = x = 54 degrees

z = 4/3*x = 4/3*54 = 72 degrees