https://file.aiquickdraw.com/mathbot/file/1726064184763n4mu0t2w.jpg

In the image, you have two intersecting lines, which form a pair of vertical angles. Vertical angles are always equal. 

In this case, the angles \((6x + 12)^\circ\) and \((10x - 8)^\circ\) are vertical angles, so we can set them equal to each other:

\[
6x + 12 = 10x - 8
\]

### Solving for \(x\):

1. Subtract \(6x\) from both sides:
   \[
   12 = 4x - 8
   \]

2. Add 8 to both sides:
   \[
   20 = 4x
   \]

3. Divide both sides by 4:
   \[
   x = 5
   \]

Thus, \(x = 5\).

Would you like more details on the steps, or do you have any questions?

Here are 5 related questions to deepen understanding:
1. What are vertical angles, and why are they equal?
2. How can you find \(x\) if the angles were supplementary instead of equal?
3. What would happen if one of the angles was expressed differently, e.g., \(5x + 15^\circ\)?
4. How can you verify the solution by substituting \(x = 5\) back into the equation?
5. What is the relationship between intersecting lines and the angles they create?

**Tip:** When solving equations with multiple variables, isolating the variable on one side often simplifies the process!

Solve for x: In the given image, two intersecting lines create vertical angles. One angle is (6x + 12)° and the other is (10x - 8)°. Set up an equation to find the value of x.

Learn how to solve for x when two vertical angles are given as (6x + 12)° and (10x - 8)°. Follow the step-by-step algebraic process to find x = 5, applying the vertical angles theorem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation