1. **Stating the problem:** We have a large triangle DFE with a right angle at H where FH is perpendicular to DE. We are given some angles and segments, and we need to find the value of the unknown angle or length related to the triangle. 2. **Identify known angles and segments:** Given angles are $\angle DFE = 100^\circ$, $\angle D = 70^\circ$, and $\angle E = 25^\circ$. The segment FH is perpendicular to DE, so $\angle FHE = 90^\circ$. 3. **Check angle sum in triangle DFE:** The sum of angles in any triangle is $180^\circ$. Let's verify: $$\angle D + \angle E + \angle F = 70^\circ + 25^\circ + 100^\circ = 195^\circ$$ This is more than $180^\circ$, so the given angles must be interpreted carefully. Since $\angle DFE = 100^\circ$ is at vertex F, and $\angle D = 70^\circ$ and $\angle E = 25^\circ$ are at vertices D and E respectively, the sum is inconsistent for triangle DFE. 4. **Re-examine the problem:** The problem likely involves smaller triangles formed by the altitude FH and segment GE. We can analyze triangle FHE, which is right-angled at H. 5. **Calculate angle FHE:** Since FH is perpendicular to DE, $\angle FHE = 90^\circ$. 6. **Use triangle FHE to find unknowns:** If $\angle E = 25^\circ$ at vertex E, then in triangle FHE: $$\angle FHE + \angle HEF + \angle EFH = 180^\circ$$ $$90^\circ + 25^\circ + \angle EFH = 180^\circ$$ $$\angle EFH = 180^\circ - 115^\circ = 65^\circ$$ 7. **Summary:** The unknown angle $\angle EFH$ is $65^\circ$. **Final answer:** $$\boxed{65^\circ}$$