What is the sum of the interior angle measures of a quadrilateral?

The sum of the interior angle measures of a **quadrilateral** is **360 degrees**. ### **Explanation:** A quadrilateral is a polygon with four sides and four interior angles. To find the sum of the interior angles of any polygon, you can use the following formula: \[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \] where \( n \) is the number of sides in the polygon. For a quadrilateral: - \( n = 4 \) Plugging the value into the formula: \[ \text{Sum of interior angles} = (4 - 2) \times 180^\circ = 2 \times 180^\circ = 360^\circ \] ### **Visualization:** Imagine dividing a quadrilateral into two triangles by drawing a diagonal. Since each triangle has interior angles that add up to 180 degrees, the quadrilateral (being composed of two triangles) will have: \[ 180^\circ + 180^\circ = 360^\circ \] This holds true for all simple (non-self-intersecting) quadrilaterals in Euclidean geometry. ### **Example:** Consider a rectangle, which is a specific type of quadrilateral. Each of its four interior angles is 90 degrees. Adding them up: \[ 90^\circ + 90^\circ + 90^\circ + 90^\circ = 360^\circ \] This confirms that the sum of the interior angles of a quadrilateral is indeed 360 degrees.