Let's say we have angles A, B, and C.

You know that two of them are x and 4x.

So let's say that A is the one that is x, and B is the one that is 4x. It doesn't matter which we choose (mathematicians use the phrase "without loss of generality" before making such assumptions, FYI).

So we have A + B + C = 180. What is C? Well, since it's an isosceles triangle, C must equal one of the other two. C must equal x OR C must equal 4x.

Start with the first case: C = x

Then A + B + C = 180 becomes

x + 4x + x = 180. Solve for x.

Second case: C = 4x

Then A + B + C = 180 becomes

x + 4x + 4x = 180. Solve for x.

Those are your two values for x!