What is the sum of the angles in a quadrilateral?

What is the sum of the angles in a quadrilateral?

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

Answer: (A)

The sum of the angles in a quadrilateral is always 360 degrees. This can be understood through the concept of dividing the quadrilateral into triangles. A quadrilateral can be divided into two triangles by drawing a diagonal between any two non-adjacent vertices. Since the sum of the angles in each triangle is 180 degrees, the total for two triangles is 180 + 180, which equals 360 degrees. This property applies to any quadrilateral, regardless of its shape, whether it's a rectangle, square, trapezoid, or any other four-sided figure. Thus, the total measure of the four interior angles in a quadrilateral consistently sums to 360 degrees, confirming why the correct answer is the first choice.

The sum of the angles in a quadrilateral is always 360 degrees. This can be understood through the concept of dividing the quadrilateral into triangles. A quadrilateral can be divided into two triangles by drawing a diagonal between any two non-adjacent vertices. Since the sum of the angles in each triangle is 180 degrees, the total for two triangles is 180 + 180, which equals 360 degrees.

This property applies to any quadrilateral, regardless of its shape, whether it's a rectangle, square, trapezoid, or any other four-sided figure. Thus, the total measure of the four interior angles in a quadrilateral consistently sums to 360 degrees, confirming why the correct answer is the first choice.