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in Mathematics by (77.4k points)

The interior angles of a polygon are in arithmetic progression. The smallest angle is 52° and the common difference is 8° . Find the number of sides of the polygon. 

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Let ‘n’ be the sides of the polygon. 

Sum of all interior angles of polygon =

But when n = 30, the last angle is 52° + (30°- 1)8° = 284° , 

Which is not possible as interior angle of a polygon cannot be more than 180°.

∴ Number of sides of given polygon is 3

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