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$The interior angles of a convex polygon forms on A.P with common$ $difference of 4^{\circ} . If the largest interior angle is 172^{\circ} then the number of sides is$

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Correct option is C

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

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$The interior angles of a convex polygon forms on A.P with common$ $difference of 4^{\circ} . If the largest interior angle is 172^{\circ} then the number of sides is$