Explanation:
remember, the sum of all angles in a triangle is always 180°.
and the sum of all angles around a single point on one side of a line is also always 180° (because the line can be seen as the diameter of a circle with the given point being its center, so, one side of the line is then a half-circle, which represents 180°).
so, the third internal angle of the triangle must be together with the given 100° = 180°.
that means the third internal angle = 180 - 100 = 80°.
and the sum of all 3 internal angles must be 180° :
x + 4x + 80 = 180
x + 4x = 100
5x = 100
x = 100/5 = 20° = angle FGN.
4x = 4×20 = 80° = angle GFN.