Math Problem Statement
Solution
The image shows a transversal cutting through two parallel lines, , with angle expressions and .
Since the lines are parallel, the two angles shown in the diagram are alternate interior angles, and therefore, they are equal.
Step-by-step solution:
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Set the two angle expressions equal to each other:
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Subtract from both sides to simplify:
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Add 9 to both sides:
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Divide by 2:
Final answer:
The value of is .
Let me know if you'd like more details or have any questions.
Follow-up questions:
- What are alternate interior angles, and how do they work with parallel lines?
- How can you check if two angles are alternate interior angles in a given figure?
- What are other types of angles formed by a transversal and parallel lines, such as corresponding angles?
- How does solving linear equations help in geometry problems involving angles?
- Can you solve for if the angles were given as consecutive interior angles instead?
Tip:
Always verify the properties of angles (alternate, corresponding, etc.) when dealing with parallel lines, as these relationships are key to solving for unknowns.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Parallel Lines
Transversals
Alternate Interior Angles
Formulas
Angle1 = Angle2 (for alternate interior angles)
Theorems
Alternate Interior Angles Theorem
Suitable Grade Level
Grades 8-10
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