Polygon Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
What is the sum of the interior angles of a hexagon?

Solution

  1. 1
    Step 1: Use the interior angle sum formula: (n−2)×180°(n-2) \times 180° where nn is the number of sides.
  2. 2
    Step 2: A hexagon has n=6n = 6 sides.
  3. 3
    Step 3: Sum =(6−2)×180°=4×180°=720°= (6-2) \times 180° = 4 \times 180° = 720°.

Answer

720°720°
Any polygon can be divided into (n−2)(n-2) triangles by drawing diagonals from one vertex. Since each triangle contributes 180°180°, the total interior angle sum is (n−2)×180°(n-2) \times 180°. For a hexagon, this gives 720°720°.

About Polygon

A closed two-dimensional figure formed by three or more straight line segments connected end-to-end.

Learn more about Polygon →

More Polygon Examples

Example 2 medium

Each interior angle of a regular polygon is [formula]. How many sides does it have?

Example 3 easy

What is the sum of the exterior angles of any convex polygon?

Example 4 hard

A polygon has an interior angle sum of [formula]. How many sides does it have?

← All Polygon Examples Polygon Concept

Related Concepts

LineAngles