Math Problem Statement
If PR and SU are parallel lines and m∠UTQ = 63°, what is m∠PQT?
Solution
We are given a diagram with parallel lines and an angle . The task is to find the measure of .
Step-by-step solution:
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Identify the relevant angles:
- The lines are cut by the transversal line , which creates alternate interior angles.
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Relation between and :
- Since and is a transversal, the angle is alternate interior with .
- Alternate interior angles are congruent when lines are parallel.
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Conclusion:
- .
Thus, the measure of is .
Would you like more details or have any questions? Here are some related questions for practice:
- What is the definition of alternate interior angles?
- How do we determine if two lines are parallel in a geometric diagram?
- If was given as , what would be?
- What role do transversals play when working with parallel lines?
- How can you use corresponding angles to solve for unknown angles in a parallel line setup?
Tip: In problems involving parallel lines and transversals, always look for congruent or supplementary angle pairs like alternate interior or corresponding angles.
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Math Problem Analysis
Mathematical Concepts
Geometry
Parallel Lines
Angles
Transversals
Formulas
m∠PQT = m∠UTQ (Alternate Interior Angles Theorem)
Theorems
Alternate Interior Angles Theorem
Suitable Grade Level
Grades 7-9