https://file.aiquickdraw.com/mathbot/file/1726144688577kz4w0hla.jpg

We are given two angles:
- \( m \angle DEF = 109^\circ \)
- \( m \angle GEF = 38^\circ \)

The task is to find \( m \angle DEG \).

From the diagram, we can see that \( \angle DEG \) is the sum of \( \angle DEF \) and \( \angle GEF \).

Thus, we can calculate:
\[
m \angle DEG = m \angle DEF - m \angle GEF
\]
Substituting the given values:
\[
m \angle DEG = 109^\circ - 38^\circ = 71^\circ
\]

So, the measure of \( m \angle DEG \) is \( 71^\circ \).

Would you like further details or have any additional questions?

Here are 5 related questions for further exploration:
1. How would you approach solving for other unknown angles in the diagram?
2. How can you verify the sum of angles in a geometric figure?
3. What would change if the angles were oriented differently?
4. What is the importance of angle subtraction in geometric proofs?
5. Can you apply the angle addition property to other types of geometric shapes?

**Tip:** Always check if the sum of angles in a problem forms a known geometric pattern, like a straight line or triangle!

Solve for m∠DEG if m∠DEF = 109° and m∠GEF = 38°.

Learn how to solve for the angle m∠DEG using the angle subtraction method. This problem involves geometric concepts such as angle addition and subtraction, and is suitable for students in Grades 6-8.

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