Which statement about exterior angles of a polygon is true?

• A. The sum of exterior angles of a polygon is always 360 degrees.
• B. The sum is equal to 180 degrees times number of sides.
• C. Each exterior angle equals 360/n.
• D. The sum is zero for polygons with parallel sides.

Answer: (A)

When you traverse a polygon and look at the exterior angle at each vertex, the total turning you do around the figure adds up to a full rotation, 360 degrees. This holds for any simple polygon, whether it’s convex or has corners that bend inward.

Here’s why: at each vertex, the interior angle and its adjacent exterior angle form a straight line, so interior plus exterior equals 180 degrees. If the polygon has n sides, the sum of all interior angles is (n − 2) × 180 degrees. Therefore, the sum of all exterior angles is n × 180 − (n − 2) × 180 = 360 degrees.

This also clarifies why the other statements aren’t generally true: the total exterior-angle sum isn’t 180 degrees times the number of sides (that would conflict with the interior sum), each exterior angle isn’t necessarily 360/n unless the polygon is regular, and the sum isn’t zero just because some sides are parallel.