angles e, f and a are supplimentary (they add up to 180). since triangles ACF and CDE are equilateral, all their angles are 60. so a = f = 60. which means that e = 180 - 2(60) = 60

again, since triangle ACF is equilateral, angle b = 60. so since b + d = 90, we have d = 90 - 60 = 30.

now the angles of a triangle add up to 180. so for triangle ABC, d + e + g = 180.

=> 30 + 60 + g = 180

=> g = 180 - 30 - 60 = 90

since one of the angles of triangle ABC is 90, it is a right-triangle