Answer :

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°.


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