Math Problem Statement

Given m || n, find the value of x. (8x-9)° and (6x+1)° are the angles formed by a transversal cutting parallel lines m and n.

Solution

The image shows a transversal cutting through two parallel lines, mnm \parallel n, with angle expressions (8x9)(8x - 9)^\circ and (6x+1)(6x + 1)^\circ.

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:

  1. Set the two angle expressions equal to each other: 8x9=6x+18x - 9 = 6x + 1

  2. Subtract 6x6x from both sides to simplify: 2x9=12x - 9 = 1

  3. Add 9 to both sides: 2x=102x = 10

  4. Divide by 2: x=5x = 5

Final answer:

The value of xx is 55.

Let me know if you'd like more details or have any questions.

Follow-up questions:

  1. What are alternate interior angles, and how do they work with parallel lines?
  2. How can you check if two angles are alternate interior angles in a given figure?
  3. What are other types of angles formed by a transversal and parallel lines, such as corresponding angles?
  4. How does solving linear equations help in geometry problems involving angles?
  5. Can you solve for xx 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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