Explanation:
This is because any pair of adjacent interior and exterior angles must add to 180 degrees. The two angles are supplementary. They form a straight line when glued together.
If x is the exterior angle, then x+174 = 180 solves to x = 6 after subtracting 174 from both sides.
Side note: This regular polygon has 360/x = 360/6 = 60 sides.
