When all the angles of a quadrilateral are added together their sum is __________ degrees.

When all the angles of a quadrilateral are added together their sum is __________ degrees.

• A. 90
• B. 120
• C. 180
• D. 360

Answer: (D)

The sum of the interior angles of a quadrilateral is always 360 degrees. This is derived from the general rule that the sum of the interior angles of any polygon can be calculated using the formula (n-2) × 180 degrees, where n is the number of sides of the polygon. For a quadrilateral, which has four sides, n equals 4. Hence, the calculation becomes (4-2) × 180 degrees = 2 × 180 degrees = 360 degrees. Knowing this basic property of quadrilaterals helps in solving various geometric problems and is foundational knowledge for fields such as engineering and architecture, where understanding shapes and their properties is crucial.

The sum of the interior angles of a quadrilateral is always 360 degrees. This is derived from the general rule that the sum of the interior angles of any polygon can be calculated using the formula (n-2) × 180 degrees, where n is the number of sides of the polygon. For a quadrilateral, which has four sides, n equals 4. Hence, the calculation becomes (4-2) × 180 degrees = 2 × 180 degrees = 360 degrees.

Knowing this basic property of quadrilaterals helps in solving various geometric problems and is foundational knowledge for fields such as engineering and architecture, where understanding shapes and their properties is crucial.