What is the sum of the angles in a quadrilateral?

What is the sum of the angles in a quadrilateral?

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

Answer: (C)

The sum of the angles in a quadrilateral is 360 degrees. This is true for any quadrilateral, regardless of whether it is convex or concave. To understand why, consider the fact that a quadrilateral can be divided into two triangles by drawing a diagonal between two of its non-adjacent vertices. Since the sum of the angles in each triangle is 180 degrees, the sum of the angles in the two triangles is 180 degrees plus 180 degrees, which equals 360 degrees. Thus, each quadrilateral will always have a total of 360 degrees for its interior angles, making this option the correct one. Other choices present incorrect sums which do not hold true for any quadrilateral.

The sum of the angles in a quadrilateral is 360 degrees. This is true for any quadrilateral, regardless of whether it is convex or concave. To understand why, consider the fact that a quadrilateral can be divided into two triangles by drawing a diagonal between two of its non-adjacent vertices. Since the sum of the angles in each triangle is 180 degrees, the sum of the angles in the two triangles is 180 degrees plus 180 degrees, which equals 360 degrees. Thus, each quadrilateral will always have a total of 360 degrees for its interior angles, making this option the correct one. Other choices present incorrect sums which do not hold true for any quadrilateral.