Math Problem Statement
Solution
This problem involves finding the value of in the context of parallel lines cut by a transversal.
Given Information:
- Two parallel lines are cut by a transversal.
- The angles formed by the intersection of the transversal with the parallel lines are:
Solution Outline:
Since , these angles are corresponding angles, and corresponding angles are congruent when parallel lines are cut by a transversal. Therefore, we can set the two angles equal to each other:
Step-by-Step Solution:
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Set up the equation:
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Simplify by subtracting from both sides:
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Add 20 to both sides:
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Solve for :
Thus, the value of is .
Would you like further details or have any questions? Here are 5 related questions to explore the concept more:
- What are corresponding angles, and why are they congruent when lines are parallel?
- How would the solution change if the angles were supplementary instead of congruent?
- What is the significance of parallel lines in this type of geometry problem?
- How do you verify if two lines are parallel in a geometry problem like this?
- Can you derive the value of if the transversal cuts the lines at different angles?
Tip: Remember that when solving for in geometry problems involving parallel lines and transversals, always check whether the angles are congruent or supplementary depending on their position.
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Math Problem Analysis
Mathematical Concepts
Geometry
Parallel Lines
Transversals
Algebra
Formulas
4x - 8 = 7x - 20
Theorems
Corresponding Angles Theorem
Congruent Angles Theorem
Suitable Grade Level
Grades 8-10
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