Show that: the sum of the interior angles of polygons with 3, 4, 5, 6, …. sides form an arithmetic progression.
To Find: The sum of the interior angles for a 21 – sided polygon.
Given: That the sum of the interior angles of a triangle is 180°.
NOTE: We know that sum of interior angles of a polygon of side n is (n – 2) x 180°.
Let an= (n – 2) x 180° ⇒ Since an is linear in n. So it forms AP with 3, 4, 5, 6,……sides
{an is the sum of interior angles of a polygon of side n}
By using the above formula, we have
a21 = (21 – 2) x 180°
a21 = 3420°

So, the Sum of the interior angles for a 21 – sided polygon is equal to 3420°.