The sum of interior angles of a polygon is 2160°. The number of sides of the…

Concept: The sum of the interior angles of an n-sided polygon is given by the formula (n − 2) × 180°, obtained by dividing the polygon into (n − 2) non-overlapping triangles drawn from one vertex, each contributing 180°.

Application: For this polygon, the sum is given as 2160°.

1. Set the formula equal to the given sum: (n − 2) × 180° = 2160°.

2. Divide both sides by 180°: n − 2 = 12.

3. Add 2 to both sides: n = 14.

Cross-check: For n = 14, (14 − 2) × 180° = 12 × 180° = 2160°, which matches the given sum — confirming the polygon has 14 sides.

Result: The polygon has 14 sides.