Math Problem Statement
Solution
To solve this problem, we are given two parallel lines, and , and two angles formed by a transversal intersecting these lines. The expressions for the angles are and .
Since the lines , the angles are corresponding angles, which means they must be equal. Therefore, we can set the two angle expressions equal to each other and solve for :
Now, let's solve this equation step by step:
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Subtract from both sides to isolate on one side:
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Add 12 to both sides to solve for :
Thus, the value of is .
Do you want more details on this solution, or do you have any questions?
Here are five related questions to deepen your understanding:
- What are alternate interior angles, and how do they relate to parallel lines?
- How would the solution change if the angles were vertical angles instead of corresponding angles?
- Can you think of a real-life example where parallel lines and transversals appear?
- What would happen if the two lines were not parallel? How would that affect the angle relationships?
- How can you verify that your solution for is correct?
Tip: Always check if the lines in the diagram are parallel before assuming angle relationships like corresponding angles or alternate interior angles.
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Math Problem Analysis
Mathematical Concepts
Geometry
Parallel Lines
Transversal
Algebra
Formulas
2x - 4 = 3x - 12
Theorems
Corresponding Angles Postulate
Suitable Grade Level
Grades 8-10