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The given problem involves angles related to parallel lines and a straight angle, and it states the following relationships:

- \(\angle ABC = \angle BAD\) because they are alternate interior angles.
- \(\angle BCA = \angle CAE\) because they are alternate interior angles.
- \(\angle BAD + x^\circ + \angle CAE = 180^\circ\) because the three angles form a straight line.

Let’s break this down:

1. \(\angle BAD + x^\circ + \angle CAE = 180^\circ\).
2. Since \(\angle ABC = \angle BAD\) and \(\angle BCA = \angle CAE\), you can substitute these angles into the equation.

Let's solve for \(x\):

\[
\angle BAD + x^\circ + \angle CAE = 180^\circ
\]

Given that \(\angle BAD = \angle CAE\), we denote \(\angle BAD = y\). The equation becomes:

\[
y + x + y = 180^\circ
\]

Simplifying:

\[
2y + x = 180^\circ
\]

Now, solve for \(x\):

\[
x = 180^\circ - 2y
\]

To find \(x\), you would need to know the specific value of \(\angle BAD\) (or \(y\)). If provided, you can substitute it into the equation to find \(x\).

Let me know if the value of \(y\) is given, or if you need further clarification!

Here are 5 relative questions for further understanding:
1. How are alternate interior angles formed between parallel lines?
2. Can you explain why the sum of the angles on a straight line equals 180°?
3. What is the relationship between adjacent angles and supplementary angles?
4. How would the equation change if you were given the value of one angle?
5. Could you explain how transversal lines interact with parallel lines?

**Tip:** In geometry, understanding angle relationships such as alternate interior angles and supplementary angles is crucial when dealing with parallel lines and transversals.

Solve for value of x in the geometric problem involving alternate interior angles.

Learn how to solve for the value of x in a geometric problem involving alternate interior angles and the sum of angles on a straight line. This solution is suitable for Grades 7-9.

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