If def is an isosceles triangle with base ef, what is the measure of f?

Step 1) Find angle FDE. This angle adds with the 66 degree angle to get 180 degrees.

(angle FDE) + 66 = 180
(angle FDE) + 66-66 = 180-66
angle FDE = 114 degrees

Step 2) Now use this to find angle E and angle F. They are congruent to each other (E = F) since EF is the base. Use the fact that all three angles of the triangle add to 180 degrees

E+F+(angle FDE) = 180
E+E+114 = 180
2E+114 = 180
2E+114-114 = 180-114
2E = 66
2E/2 = 66/2
E = 33

Since E = F, this means that F = 33 as well. 

Final Angle F is 33 degrees