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The given diagram shows two pairs of vertically opposite angles. We know that vertically opposite angles are equal.

In the diagram:

1. One pair of vertically opposite angles is:
   - \( 2x^\circ \) and \( (4x + 108)^\circ \)

Thus, we can set up the equation:
\[
2x = 4x + 108
\]

Now, let's solve for \( x \):

\[
2x - 4x = 108
\]
\[
-2x = 108
\]
\[
x = \frac{108}{-2}
\]
\[
x = -54
\]

Thus, the value of \( x \) is \( -54 \).

Would you like any further clarification or details?

Here are 5 related questions to explore:

1. What are vertically opposite angles, and why are they equal?
2. How do supplementary and complementary angles differ from vertically opposite angles?
3. If the value of \( x \) was positive, how would the angles change?
4. How can you use angle properties to solve for missing angles in polygons?
5. What is the difference between adjacent angles and vertically opposite angles?

**Tip:** Always check your answers by substituting the found value of \( x \) back into the original equation to verify.

Find the value of x in the given diagram where two pairs of vertically opposite angles are presented: 2x° and (4x + 108)°.

This problem involves finding the value of x where two vertically opposite angles are given as 2x° and (4x + 108)°. Step-by-step solution with algebraic manipulation is provided. Suitable for students in Grades 8-10.

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