Math Problem Statement
find x
Solution
This problem involves finding the value of using properties of parallel lines and angles. Here's the detailed solution:
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Understand the configuration:
- and are two parallel lines.
- and are transversals.
- The given angles are:
- , an angle formed at the intersection of and .
- , an angle formed at the intersection of and .
- , an unknown angle formed at the intersection of and .
-
Use angle relationships:
- Angles on the same side of a transversal between parallel lines are supplementary. That is:
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Solve for : Substituting :
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Verify using other angles:
- The below is vertically opposite the supplementary angle of . Since , all angle relationships are consistent.
Final Answer:
Would you like me to explain any part of this further or verify using another method?
Related Questions:
- What is the relationship between corresponding angles in this diagram?
- How would change if was altered to ?
- How can you determine if two lines are parallel using angle measurements?
- What other angle pairs are supplementary in this configuration?
- Can this concept be extended to three parallel lines? If yes, how?
Tip:
When working with parallel lines and a transversal, always look for relationships like corresponding angles, alternate angles, and supplementary angles to simplify your calculations.
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Angles
Transversals
Formulas
Supplementary angles: ∠x + ∠100° = 180°
Theorems
Angle Sum Property
Supplementary Angles Theorem
Suitable Grade Level
Grades 8-10
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