Math Problem Statement
Solution
In the given problem, lines and are parallel, and the angles provided correspond to those formed by a transversal crossing these parallel lines.
The key angles are:
Step 1: Identify Angle Relationships
Since , we can use the following angle properties:
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Alternate interior angles: These angles are equal.
- and are alternate interior angles. Therefore, we set them equal:
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Same-side interior angles: These angles are supplementary (sum to ).
- and are on the same side of the transversal, so:
Step 2: Solve for
From the first equation , solve for :
Step 3: Solve for
Substitute into the second equation:
Final Answer:
Would you like further clarification on any part of the process? Here are five related questions to explore this topic further:
- How can you use corresponding angles to solve similar problems with parallel lines and a transversal?
- What other properties of angles are useful when working with parallel lines?
- How would the solution change if the lines were not parallel?
- Can you apply these angle properties to polygons, and how?
- What are exterior angles, and how do they relate to the sum of interior angles in polygons?
Tip: Always remember that alternate interior angles are equal when two parallel lines are intersected by a transversal.
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Parallel Lines and Angles
Formulas
Alternate Interior Angles: equal angles
Same-Side Interior Angles: supplementary angles
Theorems
Alternate Interior Angle Theorem
Same-Side Interior Angle Theorem
Suitable Grade Level
Grades 8-10