Question:-What is the sum of the interior angles of an octagon?
Answer
Since an octagon is an eight-sided polygon and the sum of the interior angle of any polygon is given by the formula [n(n-3) x 180) °/n where n is the number of sides, the sum of interior angles of an octagon is 1080º. To calculate the sum of the interior angles of any polygon, we can use the formula: Hence it is a fact that the sum of the interior angle in any polygon shall be equal to (n-2) × 180 degrees, where ‘n’ is the number of sides of the polygon. In the case of the octagon, the value n will be equal to eight which is not a surprise. Substituting this value in the formula, we get: Since any polygon can be split into triangles, let this polygon be interlinked with triangles by selecting one vertex and then linking it to all the other vertices.
Using the triangle sum theorem, we have, Interior angle sum = [number of interior angles [ (8-2)] ] x 180 degrees
This gives us, Interior angle sum = 6 x 180 degrees
Interior angle sum = 1080 degrees
By these measurements, the total of the interior angles of these triangles will come out as the total sum of the interior angles of the polygon.