The sum of the interior angles in a quadrilateral is always $360$ degrees.

To understand why this is true, let’s begin by recalling that a quadrilateral is a polygon with four sides. One effective method for determining the sum of the interior angles of any polygon is to divide it into triangles, as the sum of the interior angles of a triangle is always $180$ degrees.

For a quadrilateral, you can draw a diagonal line connecting one vertex to the opposite vertex. This action divides the quadrilateral into two triangles. Since each triangle has interior angles that sum to $180$ degrees, the total sum of the angles in the two triangles becomes:

Alternatively, you can use the general formula for calculating the sum of the interior angles of a polygon, which is given by:

where $n$ represents the number of sides. For a quadrilateral, where $n = 4$, substituting this into the formula yields:

This principle holds true for all types of quadrilaterals, including squares, rectangles, trapezoids, and any other four-sided shapes. Regardless of the specific configuration, as long as a polygon has four sides, the sum of its interior angles will always equal $360$ degrees. This fundamental property of quadrilaterals is essential for solving a wide range of geometric problems.