Extended data

On a rectangular piece of paper, there were originally four corners. When we cut off a corner, the number of remaining corners will change. In order to solve this problem, we can analyze it from the perspective of geometry.

First, we need to define a rectangle. A rectangle is a special quadrilateral, in which adjacent sides are perpendicular to each other and all internal angles are right angles (90 degrees). Because the two opposite sides of a rectangle are parallel and equal, each inner angle is 90 degrees.

When we cut off a corner, we actually turn the original rectangle into an irregular quadrilateral. In this new quadrilateral, the number of remaining angles will change.

In order to better understand this problem, we can deduce it through geometric principles. First of all, we know that the sum of the internal angles of a rectangle is 360 degrees, because each internal angle is a right angle (90 degrees). When we cut off an angle, the sum of the remaining three angles is 270 degrees (90 degrees +90 degrees +90 degrees).

This question can be answered by geometric principles and mathematical deduction, without the actual paper-cutting operation. No matter how we cut paper, the essence of rectangle will not change. Therefore, no matter how you cut paper, you will come to the same conclusion: after cutting one corner, there are still three corners left on the rectangular paper.

To sum up, a rectangular piece of paper has three corners after cutting off one corner. This answer can be derived from geometric principles and mathematics, and is not affected by specific paper-cutting operations.

When we cut off a corner, we actually turn a rectangle into an irregular quadrilateral. The geometric shape and angular distribution of this quadrilateral are uncertain, but it must be a closed figure with four sides connected together.

Now, we need to consider the sum of the internal angles of the quadrilateral. According to the theorem in Euclidean geometry, the sum of internal angles of any N-sided polygon can be calculated by the formula (n-2)× 180 degrees.

However, we need to note that the new quadrilateral is not necessarily a rectangle. Because we are not sure how to cut the corner, the nature of the new figure is uncertain. Non-right angles or unequal sides may appear.