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Question

Show that the sum of the interior angles of polygons with 3,4,5,6...... sides from an arithmetic progression and find the sum of the interior angles for a 21 sided polygon .

A
1240
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B
1250
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C
3340
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D
3420
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Solution

The correct option is A 3420
We know that sum of interior angles of a polygon of side n is (n-2) x 180 so let tn =(n-2) x 180
tnislinearinn,soitisnthtermofsomeAP
t3=180,n=3
t4=2×180,n=4
t5=3×180,n=5
t4t3=180,
t5t4=180
commondiffernceis180
Sum of interior angles of polygon with 3, 4, 5, .sides forms an AP.

Now sum of interior angles of 21 sides polygon is

t21=(212)×180

19×180

3420


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