Math Problem Statement
Solution
To solve for and ensure that lines and are parallel, we need to use the fact that the corresponding angles formed by a transversal with two parallel lines must be equal.
Given:
- The angle on line is .
- The corresponding angle on line is .
For lines and to be parallel, the corresponding angles must be equal:
Now, let's solve for :
Subtract from both sides:
Subtract 24 from both sides:
Divide by 6:
The solution is:
Would you like further details or have any other questions?
Related Questions:
- What are the corresponding angles, and why do they need to be equal for lines to be parallel?
- What would happen if the value of did not satisfy this equation?
- How do we identify corresponding angles in different geometric configurations?
- Can you provide a real-world example where parallel lines and corresponding angles are relevant?
- How do different types of angles (alternate interior, exterior, etc.) behave with parallel lines?
Tip: Remember that in geometry, parallel lines have equal corresponding angles when crossed by a transversal.
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Math Problem Analysis
Mathematical Concepts
Algebra
Parallel Lines
Corresponding Angles
Formulas
9x + 24 = 3x
Theorems
Corresponding Angle Postulate
Suitable Grade Level
Grades 8-10
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