    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 3420We 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,soitisnthtermofsomeAPt3=180,n=3t4=2×180,n=4t5=3×180,n=5t4−t3=180,t5−t4=180commondiffernceis180Sum of interior angles of polygon with 3, 4, 5, .sides forms an AP.Now sum of interior angles of 21 sides polygon is t21=(21−2)×18019×180 3420  Suggest Corrections  0      Similar questions  Related Videos   Arithmetic Progression - Sum of n Terms
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