Math Problem Statement

In the figure below, m1 || m2 and m3 || m4. What is the value of x?

Solution

The diagram shows several lines and angles. Given that m1m2m_1 \parallel m_2 and m3m4m_3 \parallel m_4, we can apply properties of parallel lines and the angles they create with transversals to find xx.

  1. m1m2m_1 \parallel m_2 Property:

    • The given 4242^\circ angle formed by m2m_2 and the transversal is corresponding to the angle between m1m_1 and the transversal on the right, hence that angle is also 4242^\circ.
  2. m3m4m_3 \parallel m_4 Property:

    • Since m3m4m_3 \parallel m_4, and using the fact that m2m_2 acts as a transversal, the angle xx is alternate interior with the 4242^\circ angle at m1m_1 because they are formed between parallel lines m1m_1 and m3m_3 with m2m_2 as a transversal.

Given that xx is alternate interior with 4242^\circ, it must also be 4242^\circ.

Thus, the value of xx is 4242^\circ.

Would you like further details on any of these concepts or have any questions about this solution? Here are a few related questions you might consider:

  1. How do corresponding angles work when lines are parallel?
  2. What are alternate interior angles?
  3. Can you explain how the angle of 138138^\circ and 158158^\circ might be used or calculated in different geometric setups?
  4. How would the angle measures change if the lines were not parallel?
  5. What is the significance of transversal lines in geometry?

Tip: In problems involving parallel lines, always consider the relationship of corresponding, alternate interior, and consecutive interior angles, as these often provide the quickest path to a solution.

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallel Lines
Transversals
Corresponding Angles
Alternate Interior Angles

Formulas

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Theorems

Corresponding Angles Postulate
Alternate Interior Angles Theorem

Suitable Grade Level

Grades 8-10