We know that the sum of the interior angles of a triangle is 180°.

Question:

We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.                [NCERT EXEMPLAR]

Solution:

We know that,

the sum of the interior angles of a polygon with 3 sides, a1 = 180°,

the sum of the interior angles of a polygon with 4 sides, a2 = 360°,

the sum of the interior angles of a polygon with 5 sides, a3 = 540°,

 

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