Question

Can the sum of the interior angles of a polygon be 1530°? Justify your answer.
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Answer 1

An exterior angle of a polygon is made by extending only one of its sides, in the outward direction. The angle next to an interior angle, formed by extending the side of the polygon, is the exterior angle.

Hence, we can say, if a polygon is convex, then the sum of the degree measures of the exterior angles, one at each vertex, is 360°.

Therefore, the sum of exterior angles = 360°

Proof: For any closed structure, formed by sides and vertex, the sum of the exterior angles is always equal to the sum of linear pairs and sum of interior angles. Therefore,

S = 180n – 180(n-2)

S = 180n – 180n + 360

S = 360°

Also, the measure of each exterior angle of an equiangular polygon = 360°/n