The ratio of sum of interior angles to sum of exterior angles of a regular polygon of n sides is \frac{7}{2}. What is the measure of an interior angle of polygon?

Explanation

The sum of exterior angles of any polygon is 360^\circ. The sum of interior angles is \frac{7}{2} \times 360^\circ = 1260^\circ. For a regular n-gon, (n-2) \times 180^\circ = 1260^\circ \implies n=9. Each interior angle is \frac{1260^\circ}{9} = 140^\circ.

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