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

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

• A. 180 degrees
• B. 360 degrees
• C. 270 degrees
• D. 90 degrees

Answer: (B)

The sum of the interior angles of a quadrilateral is 360 degrees. This can be derived using the formula for the sum of the interior angles of a polygon, which is given by the formula \(180(n - 2)\), where \(n\) is the number of sides in the polygon. For a quadrilateral, there are 4 sides, so \(n = 4\). Plugging this into the formula, we get: \[ 180(4 - 2) = 180 \times 2 = 360 \text{ degrees}. \] This means that when you add all four interior angles of any quadrilateral, they will total 360 degrees, regardless of the shape of the quadrilateral. Understanding this is essential in geometry, as it lays the groundwork for more complex shapes and their properties.

The sum of the interior angles of a quadrilateral is 360 degrees. This can be derived using the formula for the sum of the interior angles of a polygon, which is given by the formula (180(n - 2)), where (n) is the number of sides in the polygon. For a quadrilateral, there are 4 sides, so (n = 4). Plugging this into the formula, we get:

[

180(4 - 2) = 180 \times 2 = 360 \text{ degrees}.

]

This means that when you add all four interior angles of any quadrilateral, they will total 360 degrees, regardless of the shape of the quadrilateral. Understanding this is essential in geometry, as it lays the groundwork for more complex shapes and their properties.