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

Solution:

A hexagon is a polygon with six sides.

An interior angle is an angle measured between the two adjacent sides of a polygon.

The sum of the interior angles of a hexagon can be calculated in two ways:

• Dividing the hexagon into triangles
• Interior angle sum formula

Dividing the hexagon into triangles

In this method, we are going to divide the hexagon into four triangles as shown below

The hexagon is divided into four triangles namely △BCA, △CDA, △DEA, △EFA

The sum of the interior angles = ∠A + ∠B + ∠C + ∠D + ∠E + ∠F

= (∠BAC + ∠CAD + ∠DAE + ∠FAE ) + ∠B + (∠BCA + ∠DCA) + (∠CDA + ∠EDA) + (∠AEF + ∠AED) + ∠F

= (∠BAC + ∠B + ∠BCA) + (∠CAD + ∠DCA + ∠CDA ) + (∠EDA + ∠DAE + ∠AED)  + ( ∠AEF + ∠FAE + ∠F) (Rearranging the terms)

= Sum of interior angles of △BCA + Sum of interior angles of △CDA + Sum of interior angles of △DEA + Sum of interior angles of △EFA

= 180° + 180° + 180° + 180°  (Since, sum of interior angles of a triangle is 180°)

= 720°

Interior angle sum formula:

Sum of interior angles of a Polygon = (n - 2) × 180°

where n = number of sides

For a hexagon, n = 6

Thus, by substituting in the above formula we get

Sum of interior angles of a hexagon = (6 - 2) × 180° = 720°

Thus, the sum of the interior angles of a hexagon is 720°.

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

Summary:

The sum of the interior angles of a hexagon is 720°