The interior anglesof a polygon are in
a.P. The smallest angle is 52and the common difference is 8. Find the number of sides of the polygon.
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Sn =n÷2(2a+(n-1)d
Sn =(n-2)180
therefore,
180n-360=n÷2(2×52+(n-1)8
2(180n-360)=n(104+8n-8)
360n-720=96n+8n2
360-96n-720=8n2
274n-720-8n2=0
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