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 with3,4,5,6..Sides form an arithmetic progression .Find the sum of the interior angles for a 21 sided polygon

Answer 1

Answer:

The arithmetic progression: Sum of the interior angles of the polygon= 180(n-2) degrees

Step-by-step explanation:

Sum of the interior angles of a triangle = 180( 3-sided)

Sum of the interior angles of a quadrilateral= 360(4-sided). We can say this because we can form two triangles within a quadrilateral

Similarly,

Sum of the interior angles of a pentagon= 540( 180x3)

Sum of the interior angles of a hexagon= 720(180x4)

Now,from the above statements,

The number of triangles within a n-sided polygon = n-2

Sum of the interior angles of the polygon= 180(n-2) degrees

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For 21-sided polygon,the sum of its interior angles is:
180(21-2)= 180(19)=3240 degrees