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

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

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

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