The solution to the problem involves analyzing the triangle and its internal angles:

1. Value of $g$:

   • The angles in a triangle sum up to $180^\circ$. For the smaller triangle at the top: $g + 11^\circ + e = 180^\circ.$ Rearranging for $g$: $g = 180^\circ - 11^\circ - e.$

2. Value of $e$:

   • In the lower triangle, the angles also sum to $180^\circ$. Therefore: $66^\circ + 108^\circ + e = 180^\circ.$ Solving for $e$: $e = 180^\circ - 66^\circ - 108^\circ = 6^\circ.$

3. Substitute $e = 6^\circ$ to find $g$: $g = 180^\circ - 11^\circ - 6^\circ = 163^\circ.$

4. Value of $f$:

   • For the smaller triangle, the two angles $f$ and $e$ are on a straight line, so they sum to $180^\circ$: $f + 108^\circ = 180^\circ.$ Solving for $f$: $f = 180^\circ - 108^\circ = 72^\circ.$

Final Answers:

• $e = 6^\circ$
• $g = 163^\circ$
• $f = 72^\circ$