Is This One Obvious?

One of the solutions is obvious, $x=30^\circ$ , with the overall triangle being equilateral. But there is a second solution.

To find it, let’s concentrate on the triangle $\triangle ABE$ . $\angle EAB=\angle EBG=30^\circ$ . Also $AG=2\times GE$ . Such a triangle can be constructed in an alternative way as shown below.

The rest of the $\triangle ABC$ can be easily shown to exist. The angle $x=90^\circ$ , so the average, and therefore the answer, is $60^\circ$ .