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 PRSUPR \parallel SU and an angle mUTQ=63m\angle UTQ = 63^\circ. The task is to find the measure of mPQTm\angle PQT.

Step-by-step solution:

  1. Identify the relevant angles:

    • The lines PRSUPR \parallel SU are cut by the transversal line TQTQ, which creates alternate interior angles.
  2. Relation between UTQ\angle UTQ and PQT\angle PQT:

    • Since PRSUPR \parallel SU and TQTQ is a transversal, the angle UTQ\angle UTQ is alternate interior with PQT\angle PQT.
    • Alternate interior angles are congruent when lines are parallel.
  3. Conclusion:

    • mPQT=mUTQ=63m\angle PQT = m\angle UTQ = 63^\circ.

Thus, the measure of mPQTm\angle PQT is 63\boxed{63^\circ}.

Would you like more details or have any questions? Here are some related questions for practice:

  1. What is the definition of alternate interior angles?
  2. How do we determine if two lines are parallel in a geometric diagram?
  3. If mUTQm\angle UTQ was given as 4545^\circ, what would mPQTm\angle PQT be?
  4. What role do transversals play when working with parallel lines?
  5. 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