Math Problem Statement

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 ∘ .

Solution

We are given the following information:

  • mDEF=109m\angle DEF = 109^\circ
  • mGEF=38m\angle GEF = 38^\circ

We are asked to find mDEGm\angle DEG.

Step-by-step solution:

  1. Relationship between the angles: Since DD, EE, FF, and GG are points forming angles, we need to observe that: mDEG=mDEFmGEFm\angle DEG = m\angle DEF - m\angle GEF This is because the angles DEFDEF and GEFGEF share a common angle at EE, and DEGDEG is the remaining part.

  2. Substitute the values: Using the given information: mDEG=10938=71m\angle DEG = 109^\circ - 38^\circ = 71^\circ

Thus, mDEG=71m\angle DEG = 71^\circ.

Would you like further details or have any questions?


Here are 5 related questions to deepen your understanding:

  1. What is the sum of all angles around point EE?
  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 GEFGEF changes, how would that affect angle DEGDEG?

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

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Math Problem Analysis

Mathematical Concepts

Angle Subtraction
Geometry
Linear Angles

Formulas

m∠DEG = m∠DEF - m∠GEF

Theorems

Angle Addition Postulate

Suitable Grade Level

Grades 6-8