What is the total measure of the interior angles of a quadrilateral?

The total measure of the interior angles of a quadrilateral is 360 degrees. To understand why this is the case, consider that a quadrilateral is a four-sided polygon. The general formula for calculating the sum of the interior angles of any polygon is given by the formula:

[ \text{Sum of interior angles} = (n - 2) \times 180

]

where ( n ) is the number of sides in the polygon. For a quadrilateral, ( n ) is 4. Plugging in the value:

[ (4 - 2) \times 180 = 2 \times 180 = 360 ]

Therefore, the total measure of the interior angles in a quadrilateral is indeed 360 degrees. This fundamental property is consistent across all quadrilaterals, regardless of their shape—whether a square, rectangle, trapezoid, or any other four-sided figure.