Solve for m, angle, D, E, Gm∠DEG if m, angle, D, E, F, equals, 109, degreesm∠DEF=109 
∘
  and m, angle, G, E, F, equals, 38, degreesm∠GEF=38 
∘
 .

We are given the following information:

- \( m\angle DEF = 109^\circ \)
- \( m\angle GEF = 38^\circ \)

We are asked to find \( m\angle DEG \).

### Step-by-step solution:

1. **Relationship between the angles**: 
   Since \( D \), \( E \), \( F \), and \( G \) are points forming angles, we need to observe that:
   \[
   m\angle DEG = m\angle DEF - m\angle GEF
   \]
   This is because the angles \( DEF \) and \( GEF \) share a common angle at \( E \), and \( DEG \) is the remaining part.

2. **Substitute the values**:
   Using the given information:
   \[
   m\angle DEG = 109^\circ - 38^\circ = 71^\circ
   \]

Thus, \( m\angle DEG = 71^\circ \).

Would you like further details or have any questions?

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Here are 5 related questions to deepen your understanding:

1. What is the sum of all angles around point \( E \)?
2. How do we classify angles if they are supplementary?
3. Can you explain the difference between adjacent and opposite angles?
4. How does the concept of linear pairs apply to this problem?
5. If angle \( GEF \) changes, how would that affect angle \( DEG \)?

**Tip:** When solving for an unknown angle, consider whether angles are complementary, supplementary, or form a straight line. This can simplify your calculations!

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

Discover how to solve for angle DEG using angle subtraction when given angles DEF and GEF. This detailed step-by-step explanation covers key geometry concepts, focusing on linear angles and angle addition postulates. Suitable for students in Grades 6-8.

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