1. The problem involves finding the values of angles $h$, $g$, and $f$ formed by two intersecting lines with given angles $100^\circ$ and $33^\circ$. 2. Vertically opposite angles are equal, so the angle opposite $100^\circ$ is also $100^\circ$. 3. Similarly, the angle opposite $33^\circ$ is also $33^\circ$. 4. Adjacent angles on a straight line sum to $180^\circ$. 5. Therefore, $h$ is adjacent to $33^\circ$, so $h = 180^\circ - 33^\circ = 147^\circ$. 6. Angle $g$ is adjacent to $100^\circ$, so $g = 180^\circ - 100^\circ = 80^\circ$. 7. Angle $f$ is vertically opposite to $h$, so $f = h = 147^\circ$. Final answers: $$h = 147^\circ, \quad g = 80^\circ, \quad f = 147^\circ$$