Math Problem Statement
ABCD is a parallelogram. Find ∠CFG. Given that ∠AEB = 65° and ∠CFE = 18°.
Solution
In the given parallelogram , we are tasked with finding .
Steps to Solve:
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Identify the angles in the diagram:
- is a parallelogram, which implies opposite sides are parallel, and the corresponding angles are equal.
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Using angle relationships:
- Since is a parallelogram, and is a transversal. Therefore, (or ) is supplementary to , because they are on the same side of the transversal .
- Supplementary angles sum to , so:
Thus, .
Would you like more details or have any further questions?
Related questions:
- What are the properties of a parallelogram in terms of angles and sides?
- How do transversal lines affect angles in parallel line systems?
- Can you explain the concept of supplementary angles?
- What is the relationship between alternate interior angles in parallelograms?
- How do you calculate unknown angles using given angles and geometric properties?
Tip: In a parallelogram, opposite angles are always equal, and adjacent angles are supplementary (add up to ).
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Math Problem Analysis
Mathematical Concepts
Geometry
Angles in Parallelograms
Transversals
Formulas
Supplementary Angles: ∠A + ∠B = 180°
Theorems
Properties of Parallelograms
Supplementary Angles Theorem
Suitable Grade Level
Grades 8-10