https://file.aiquickdraw.com/mathbot/file/1727988605704vwunbtw2.jpg

The problem involves a quadrilateral \(DGFE\), and you're asked to determine the measure of \(\angle DFG\) given that \(\angle DFE = 34^\circ\).

### Step-by-step solution:

1. **Symmetry observation:**
   The diagram suggests symmetry. Given that the angles at \(G\) and \(E\) seem to mirror each other, we can assume that \(\angle DFE\) and \(\angle DFG\) are related geometrically.

2. **Isosceles triangle (based on symmetry):**
   Since \(\triangle DFG\) appears isosceles (because the legs \(DG\) and \(DF\) seem equal in length based on symmetry), \(\angle DFG\) will be half of the remaining angle not covered by \(\angle DFE\).

3. **Triangle angle sum:**
   In \(\triangle DFG\), the sum of angles must be \(180^\circ\). The total angles at \(F\) and \(E\) should equal \(180^\circ - 34^\circ = 146^\circ\).

4. **Conclusion:**
   As \(\triangle DFG\) appears isosceles, \(\angle DFG = 17^\circ\) (half of the remaining angle of \(146^\circ\)).

Thus, the correct answer is:
\[
\boxed{17^\circ}
\]
### Answer: \(d.\) 17°

Do you need further clarification or have any questions? 

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Here are 5 related questions to explore further:
1. What would happen if \(\angle DFE\) was 40°? How would \(\angle DFG\) change?
2. Could this problem be solved using trigonometry?
3. Is it possible that \(\triangle DFG\) is not isosceles? How would that affect the solution?
4. How do we find the interior angle sum of a quadrilateral like \(DGFE\)?
5. How does symmetry help in solving geometric problems?

**Tip:** In geometry, identifying symmetry or congruent parts of a figure can often simplify complex problems significantly!

Solve the problem of finding m∠DFG in a quadrilateral where m∠DFE = 34°. This involves applying the properties of isosceles triangles and the sum of angles in a triangle. Suitable for middle school students learning geometry.

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