Check the picture below
notice, that running a line from the center, you end up with an angle bisector to a vertex of the triangle, now, this is a "regular polygon", so, all sides are equal, for a triangle, when all sides are equal, all angles are also equal, and since the sum of all internal angles in a triangle must add up to 180°, then that means, each angle is 60°
now, you run an angle bisector through it, you end up with a 30°, 30° split, and that gives you a 30-60-90 triangle
notice, that running a line from the center, you end up with an angle bisector to a vertex of the triangle, now, this is a "regular polygon", so, all sides are equal, for a triangle, when all sides are equal, all angles are also equal, and since the sum of all internal angles in a triangle must add up to 180°, then that means, each angle is 60°
now, you run an angle bisector through it, you end up with a 30°, 30° split, and that gives you a 30-60-90 triangle