A regular polygon of N sides is such that each interior angle is 120 degree greater than the exterior angle find: (1) the value of N (2) the sum of all Te interior angle

Answer 1

The sum of all exterior angles of a polygon is 360°.

If the polygon has N sides, then 360/N represents the measure of one exterior angle.

The sum of the interior angles of a regular polygon of N sides is 180(N-2). Divide that expression by N to get a representation of the measure of a single interior angle: [180(N-2)]/N.

Each interior angle is 120 more than a single exterior angle:

[180(N-2)]/N = 360/N + 120

Multiply every term by N (N > 0):

180(N-2) = 360 +120N

180N - 360 = 120N + 360

60N = 720

N = 12

180(10) = 1800

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