Q.

The interior angles of a convex polygon forms on A.P with common  difference of 4∘. If the largest interior angle is 172∘ then the number of sides is

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a

10

b

11

c

12

d

8

answer is C.

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Detailed Solution

Let n- be the number of sides of a polygontn=a+(n−1)d=172→a+4(n−1)=172→a=172−4(n−1)−⋯−1Sn=n2[a+172]=(n−2)(180)−−−2  since sum of the interior angles of a 'n'sided polygon=n-2180° From 1 and 2⇒n=12.
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The interior angles of a convex polygon forms on A.P with common  difference of 4∘. If the largest interior angle is 172∘ then the number of sides is