The problem involves two parallel lines (A and B) being cut by a transversal. The angles formed on the same side of the transversal are exterior angles, which sum up to 180° because the lines are parallel (this follows from the consecutive exterior angle theorem).

The given angles are:

1. One angle is $5x$.
2. The other angle is $150^\circ$.

Since these angles are on the same side of the transversal, their sum is $180^\circ$.

We can set up the equation as: $5x + 150 = 180$

Now, let's solve for $x$:

$5x = 180 - 150$ $5x = 30$ $x = \frac{30}{5} = 6$

Thus, $x = 6$.

Do you want more details or have any other questions?

5 Related Questions:

1. What are alternate interior angles, and how do they relate to parallel lines?
2. How would the equation change if the second angle was $(180 - 5x)$ instead of $150^\circ$?
3. What other theorems are related to angles formed by a transversal with parallel lines?
4. Can the same method be applied if the lines were not parallel? Why or why not?
5. What if the angle opposite $150^\circ$ was given? How would the equation change?

Tip:

In geometry, identifying angle pairs like alternate, corresponding, or consecutive can quickly reveal relationships and simplify solving problems involving parallel lines and transversals.