Which expression represents the sum of interior angles of a five-sided polygon?

Which expression represents the sum of interior angles of a five-sided polygon?

• A. 540
• B. 360
• C. 720
• D. 180

Answer: (A)

To find the total of interior angles for any polygon, you can think of dividing the shape into triangles. A polygon with n sides can be partitioned into n-2 triangles, and each triangle has interior angles that sum to 180 degrees. So the total is (n-2) × 180 degrees. For a five-sided figure, that’s (5-2) × 180 = 3 × 180 = 540 degrees. The other numbers don’t fit because 360 is for four sides, 720 is for six sides, and 180 is just the sum of angles in a single triangle, not a pentagon.

To find the total of interior angles for any polygon, you can think of dividing the shape into triangles. A polygon with n sides can be partitioned into n-2 triangles, and each triangle has interior angles that sum to 180 degrees. So the total is (n-2) × 180 degrees. For a five-sided figure, that’s (5-2) × 180 = 3 × 180 = 540 degrees. The other numbers don’t fit because 360 is for four sides, 720 is for six sides, and 180 is just the sum of angles in a single triangle, not a pentagon.