Math Problem Statement

Solve for x to make lines A and B parallel, where the angle on line A is 9x + 24, and the corresponding angle on line B is 3x.

Solution

To solve for xx and ensure that lines AA and BB are parallel, we need to use the fact that the corresponding angles formed by a transversal with two parallel lines must be equal.

Given:

  • The angle on line AA is 9x+249x + 24.
  • The corresponding angle on line BB is 3x3x.

For lines AA and BB to be parallel, the corresponding angles must be equal: 9x+24=3x9x + 24 = 3x

Now, let's solve for xx:

9x+24=3x9x + 24 = 3x

Subtract 3x3x from both sides:

6x+24=06x + 24 = 0

Subtract 24 from both sides:

6x=246x = -24

Divide by 6:

x=4x = -4

The solution is: x=4x = -4

Would you like further details or have any other questions?

Related Questions:

  1. What are the corresponding angles, and why do they need to be equal for lines to be parallel?
  2. What would happen if the value of xx did not satisfy this equation?
  3. How do we identify corresponding angles in different geometric configurations?
  4. Can you provide a real-world example where parallel lines and corresponding angles are relevant?
  5. How do different types of angles (alternate interior, exterior, etc.) behave with parallel lines?

Tip: Remember that in geometry, parallel lines have equal corresponding angles when crossed by a transversal.

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Math Problem Analysis

Mathematical Concepts

Algebra
Parallel Lines
Corresponding Angles

Formulas

9x + 24 = 3x

Theorems

Corresponding Angle Postulate

Suitable Grade Level

Grades 8-10