Math Problem Statement
Solution
Let's analyze the problem step by step.
We are given a figure where is a transversal of the parallel lines , , , and . The angles formed by the transversal with these lines are labeled as , , and .
Understanding the Relationships:
- Alternate Interior Angles: These angles are equal when a transversal crosses parallel lines.
- Corresponding Angles: These angles are also equal when a transversal crosses parallel lines.
- Linear Pair: The angles on a straight line sum up to 180°.
Step 1: Use Alternate Interior Angles
Since and is the transversal:
- The angle is alternate to the angle .
So, .
Step 2: Use Linear Pair
Given that the angle between lines and on the transversal is , and the adjacent angle is , we can write:
Step 3: Conclude for
Since , it follows that:
Final Answer:
The correct values of and are and . Therefore, the correct answer is:
Would you like more details on any part of the solution?
Relative Questions:
- How do alternate interior angles relate to parallel lines?
- What is the significance of corresponding angles in parallel lines?
- Can you explain how the linear pair relationship works in this problem?
- How would the solution change if were given instead of ?
- What are some other properties of transversals with parallel lines?
Tip:
When working with parallel lines and a transversal, always look for alternate interior angles and corresponding angles first, as these relationships can simplify the problem significantly.
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Math Problem Analysis
Mathematical Concepts
Geometry
Parallel Lines
Transversals
Alternate Interior Angles
Corresponding Angles
Linear Pair
Formulas
-
Theorems
Alternate Interior Angles Theorem
Suitable Grade Level
Grades 7-9
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