Math Problem Statement

If m∠DFE = 34°, then what is m∠DFG?

Solution

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

Step-by-step solution:

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

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

  3. Triangle angle sum: In DFG\triangle DFG, the sum of angles must be 180180^\circ. The total angles at FF and EE should equal 18034=146180^\circ - 34^\circ = 146^\circ.

  4. Conclusion: As DFG\triangle DFG appears isosceles, DFG=17\angle DFG = 17^\circ (half of the remaining angle of 146146^\circ).

Thus, the correct answer is: 17\boxed{17^\circ}

Answer: d.d. 17°

Do you need further clarification or have any questions?


Here are 5 related questions to explore further:

  1. What would happen if DFE\angle DFE was 40°? How would DFG\angle DFG change?
  2. Could this problem be solved using trigonometry?
  3. Is it possible that DFG\triangle DFG is not isosceles? How would that affect the solution?
  4. How do we find the interior angle sum of a quadrilateral like DGFEDGFE?
  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!

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles in a Triangle
Isosceles Triangle
Symmetry

Formulas

Sum of interior angles in a triangle: 180°

Theorems

Isosceles Triangle Theorem
Triangle Angle Sum Theorem

Suitable Grade Level

Grades 6-8