In this image, we have two parallel lines $m$ and $n$ intersected by a transversal line. The angles given are $(9x - 8)^\circ$ and $(4x + 22)^\circ$.

Since the lines are parallel, the two angles formed are alternate interior angles, which means they are equal. Therefore, we can set up the following equation:

$9x - 8 = 4x + 22$

Solving the Equation

1. Rearrange the equation to bring like terms together: $9x - 4x = 22 + 8$ $5x = 30$

2. Solve for $x$: $x = \frac{30}{5} = 6$

Answer

The value of $x$ is $6$.

Would you like more details or have any questions about the solution?

Related Questions

1. What are alternate interior angles, and why are they equal when lines are parallel?
2. How would the problem change if the lines $m$ and $n$ were not parallel?
3. What is the value of the angles when $x = 6$?
4. How can you identify which angles are alternate interior in a transversal setup?
5. What other angle relationships exist in a transversal, such as corresponding angles?

Tip

Remember that when a transversal crosses two parallel lines, alternate interior angles are always congruent!