To determine the value of \( x = \angle ABC \) in the trapezoid, we'll consider the relationship between the angles of a trapezoid.

### Given:
- \( ABCD \) is a trapezoid.
- The bases \( AB \) and \( CD \) are parallel.
- The angles at \( B \) and \( C \) are \( \angle ABC = x \) and \( \angle BCD = y \), respectively.

### Key Relationship:
- In a trapezoid, the sum of the interior angles between the parallel sides is always supplementary:
  \[
  x + y = 180^\circ
  \]

### Calculation:
If \( y = \angle BCD \) is known, you can find \( x \) as:
\[
x = 180^\circ - y
\]

### Without Specific Values:
Since the image does not specify the measure of \( y = \angle BCD \), \( x \) is simply:
\[
x = 180^\circ - y
\]

If you know \( y \), you can substitute it into this formula to find \( x \). For example, if \( y = 120^\circ \), then:
\[
x = 180^\circ - 120^\circ = 60^\circ
\]

Do you have the measure of \( \angle BCD \) (i.e., \( y \)) to calculate \( x \)?

### Additional Related Questions:
1. What is the specific measure of \( \angle BCD \)?
2. How can you verify that the angles are supplementary in a trapezoid?
3. What are the steps to calculate unknown angles in any trapezoid?
4. How do parallel sides in a trapezoid affect its angle measures?
5. How would you find \( x \) if the trapezoid was an isosceles trapezoid?

### Tip:
Always check if a given trapezoid is isosceles, as in such cases, the base angles (angles at each base) are equal.

Learn how to determine the value of angle x = ∠ABC in trapezoid ABCD using the angle sum property. Understand the relationship between angles in a trapezoid with parallel sides AB and CD. Suitable for Grades 7-9.

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