Math Problem Statement
Solution
The problem is asking to find the value of such that line is parallel to line , and to state the converse used.
From the image, we see two angles:
These angles appear to be corresponding angles since they are on the same side of the transversal and in the same relative positions.
Step-by-step solution:
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Corresponding Angles Postulate (Converse):
- If two corresponding angles are equal, then the two lines are parallel.
- So, we can set the angles equal to each other:
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Solve for : Subtract from both sides: Add 23 to both sides: Divide both sides by 5:
Converse Used:
The converse of the Corresponding Angles Postulate states that if two corresponding angles are congruent, then the lines are parallel.
Final Answer:
- The value of is 12.
- The converse used is the Corresponding Angles Postulate.
Would you like further details or explanations? Here are some related questions:
- What are corresponding angles, and why are they important for parallel lines?
- What other angle relationships (such as alternate interior angles) could help prove lines are parallel?
- How do you verify that two lines are parallel using a transversal and angle relationships?
- Can the same problem be solved using a different postulate or theorem?
- What are other converses related to angle postulates in geometry?
Tip: When working with parallel lines and a transversal, remember to check the type of angles formed (corresponding, alternate interior, etc.) to determine relationships.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Parallel Lines
Corresponding Angles
Formulas
9x + 37 = 14x - 23
Theorems
Corresponding Angles Postulate (Converse)
Suitable Grade Level
Grades 8-10