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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.

Follow the steps below to find the value of x that makes A || B. Set the sum of same side exterior angles equal to 180.

Learn how to find the value of x using the same side exterior angles theorem for parallel lines. This problem involves angles formed by a transversal intersecting parallel lines, and the sum of same side exterior angles is set to 180°. Suitable for students in Grades 8-10.

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