What is the sum of the interior angles in a quadrilateral?

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

To understand why this is the case, let's start by recalling that a quadrilateral is a four-sided polygon. One way to determine the sum of the interior angles of any polygon is to divide it into triangles, because the sum of the interior angles of a triangle is always 180 degrees.

For a quadrilateral, you can draw a diagonal line from one vertex to the opposite vertex, effectively splitting the quadrilateral into two triangles. Since each triangle has interior angles that add up to 180 degrees, the two triangles together will have angles that sum to 2 × 180 degrees, which equals 360 degrees.

Another way to think about it is by using the formula for the sum of the interior angles of a polygon, which is (n - 2) × 180 degrees, where n is the number of sides. For a quadrilateral, n is 4. Plugging this into the formula gives us (4 - 2) × 180 degrees = 2 × 180 degrees = 360 degrees.

This principle applies to all quadrilaterals, whether they are squares, rectangles, trapeziums, or any other type. No matter the shape, as long as it has four sides, the sum of its interior angles will always be 360 degrees. This is a fundamental property of quadrilaterals and is very useful in solving various geometric problems.