https://file.aiquickdraw.com/mathbot/file/1727055869244w6ffkcly.jpg

The problem involves vertical angles. Based on the image, two intersecting lines form angles labeled as \( 5x + 40^\circ \) and \( 56^\circ \), and another angle is represented by \( 3x + 60^\circ \). Vertical angles are always equal, so:

- The angle \( 5x + 40^\circ \) is vertically opposite to the \( 56^\circ \) angle.
- Using this relationship, we can set up the equation:

\[
5x + 40 = 56
\]

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

\[
5x = 56 - 40
\]
\[
5x = 16
\]
\[
x = \frac{16}{5}
\]
\[
x = 3.2
\]

Thus, \( x = 3.2 \).

If you need further clarification or want to explore more concepts related to this, feel free to ask!

### Related Questions:
1. What are vertical angles, and why are they always equal?
2. How can you verify the solution by calculating the angles explicitly?
3. Are there any other pairs of vertical angles in this diagram?
4. What is the relationship between adjacent angles when two lines intersect?
5. How do we solve similar problems with different algebraic expressions for the angles?

### Tip:
Always double-check by substituting the value of \( x \) back into the original expressions to ensure the angles are equal.

The problem involves solving for x using vertical angles: 5x + 40° and 56°, along with another expression 3x + 60°.

Learn how to solve for x using vertical angles in the geometry problem 5x + 40° = 56°. This problem involves setting up a linear equation and solving for the unknown variable. Suitable for students in Grades 7-9.

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