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:
We are asked to find .
Step-by-step solution:
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Relationship between the angles: Since , , , and are points forming angles, we need to observe that: This is because the angles and share a common angle at , and is the remaining part.
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Substitute the values: Using the given information:
Thus, .
Would you like further details or have any questions?
Here are 5 related questions to deepen your understanding:
- What is the sum of all angles around point ?
- How do we classify angles if they are supplementary?
- Can you explain the difference between adjacent and opposite angles?
- How does the concept of linear pairs apply to this problem?
- If angle changes, how would that affect angle ?
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