To find the value of \( x \), we need to look at the angles related to the cut corner of the rectangle when it transforms into a trapezoid.
Let's break down the problem:
1. Understanding the Angles in a Rectangle:
- A rectangle has four right angles, each measuring \( 90^\circ \).
- The sum of the interior angles in a rectangle is \( 360^\circ \).
2. Effect of Cutting a Corner:
- When a corner of the rectangle is cut off, one of the \( 90^\circ \) angles is effectively removed.
- The new angles formed by this cut must add up to \( 90^\circ \) to maintain the overall geometry.
3. Sum of Angles in a Trapezoid:
- The resulting shape is a trapezoid. A trapezoid, like any quadrilateral, has angles that sum up to \( 360^\circ \).
4. Forming the New Angle:
- Consider what happens to the angles around the cut corner.
- The sum of the angles around the position where the corner was cut must still add up to \( 360^\circ \) to keep the shape closed.
Given the choices and understanding that the new angles should sum up properly, the angle \( x \) created by the cutting of the corner is:
[tex]\[
x = \boxed{135^\circ}
\][/tex]
