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In the given diagram, you have two intersecting lines that form angles around point \( E \). These angles are:

- \( \angle AEB = 5x^\circ \)
- \( \angle CED = 65^\circ \)

Since these two angles are vertically opposite, they are congruent. This property allows us to set up the following equation:

\[
5x = 65
\]

To solve for \( x \), divide both sides of the equation by 5:

\[
x = \frac{65}{5} = 13
\]

Thus, the value of \( x \) is 13.

Would you like more details, or do you have any other questions?

Here are five related questions to deepen your understanding:
1. What are vertically opposite angles, and why are they always equal?
2. Can you explain how angles on a straight line add up to 180°?
3. What other properties of angles are useful when two lines intersect?
4. How would the equation change if one of the angles were given as \( (6x + 10)^\circ \)?
5. How can you apply this knowledge to solve for missing angles in parallel line problems?

**Tip:** Always remember that vertically opposite angles formed by two intersecting lines are equal, a useful property when solving for unknown angles!

Which equation can be used to solve for x in the given diagram?

Learn how to solve for x in a diagram featuring intersecting lines. This problem utilizes the property of vertically opposite angles, where two angles are congruent. A simple algebraic equation is formed and solved step-by-step.

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