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This image shows two intersecting lines forming a pair of vertical angles. One angle is given as \( (17x - 45)^\circ \), and the other angle is labeled as \( 108^\circ \).

Since the angles are vertical angles, they must be congruent. Therefore, we can set up the following equation:

\[
17x - 45 = 108
\]

### Steps to solve for \( x \):

1. Add 45 to both sides to isolate the term with \( x \):
\[
17x = 108 + 45
\]
\[
17x = 153
\]

2. Divide both sides by 17:
\[
x = \frac{153}{17}
\]
\[
x = 9
\]

So, \( x = 9 \).

If you have any questions or want further details, feel free to ask! Here are some related questions:

1. How do we identify vertical angles?
2. Can two vertical angles ever be different from each other?
3. What is the formula for solving equations involving variables?
4. How would the solution change if the angles were supplementary instead of congruent?
5. What are alternate interior angles, and how do they differ from vertical angles?

**Tip**: Vertical angles are always equal in measure, no matter how the lines are drawn, because they are opposite angles formed by two intersecting lines.

This image shows two intersecting lines forming a pair of vertical angles. One angle is given as (17x - 45)°, and the other angle is labeled as 108°. Find the value of x.

Learn how to solve for x when given two vertical angles, one as (17x - 45)° and the other as 108°. This problem demonstrates the use of algebra and the Vertical Angles Theorem to find the value of x, suitable for students in grades 8 to 10.

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