Math Problem Statement

find x

Find x.

Solution

This problem involves finding the value of xx using properties of parallel lines and angles. Here's the detailed solution:

  1. Understand the configuration:

    • aa and bb are two parallel lines.
    • ll and mm are transversals.
    • The given angles are:
      • 100\angle 100^\circ, an angle formed at the intersection of ll and aa.
      • 80\angle 80^\circ, an angle formed at the intersection of ll and bb.
      • x\angle x, an unknown angle formed at the intersection of mm and aa.
  2. Use angle relationships:

    • Angles on the same side of a transversal between parallel lines are supplementary. That is: 100+x=180\angle 100^\circ + \angle x = 180^\circ
  3. Solve for xx: Substituting 100\angle 100^\circ: x=180100=80x = 180^\circ - 100^\circ = 80^\circ

  4. Verify using other angles:

    • The 80\angle 80^\circ below is vertically opposite the supplementary angle of x\angle x. Since x=80x = 80^\circ, all angle relationships are consistent.

Final Answer:

x=80x = 80^\circ

Would you like me to explain any part of this further or verify using another method?


Related Questions:

  1. What is the relationship between corresponding angles in this diagram?
  2. How would xx change if 100\angle 100^\circ was altered to 120120^\circ?
  3. How can you determine if two lines are parallel using angle measurements?
  4. What other angle pairs are supplementary in this configuration?
  5. Can this concept be extended to three parallel lines? If yes, how?

Tip:

When working with parallel lines and a transversal, always look for relationships like corresponding angles, alternate angles, and supplementary angles to simplify your calculations.

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Math Problem Analysis

Mathematical Concepts

Parallel Lines
Angles
Transversals

Formulas

Supplementary angles: ∠x + ∠100° = 180°

Theorems

Angle Sum Property
Supplementary Angles Theorem

Suitable Grade Level

Grades 8-10