Let x be the measure of angle FED, which is the angle in red adjacent to the 108 degree angle. These two angles add to 180, so,
x+108 = 180
x+108-108 = 180-108
x = 72
Angle FED is 72 degrees. So is angle FDE as the two angles have the same angle marker to indicate they are congruent angles.
------------
We know two of the angles of triangle FED are 72 and 72. The missing angle 'u' is added to the two angles and we set the sum equal to 180 to get this equation
72+72+u = 180
Let's solve for the variable 'u' to get
72+72+u = 180
144+u = 180
144+u-144 = 180-144
u = 36
-------------
Answer: 36