The Sum of The Interior Angles of a Hexagon


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

hexagon is a polygon with six sides.

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

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

Explanation:

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

  • Dividing hexagon into triangles
  • Interior angle sum formula

Dividing hexagon into triangles

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

interior angles of an hexagon

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°.