line BC in one side of a regular n-gon. the sides next to line BC are extended to meet at point W. Find the measure of angle W in terms of n.

Answer 1

The exterior angles of a regular n-gon are all 360/n degrees.

They form the base angles B and C of an isosceles triangle with apex at W.

So, 360/n + 360/n + W = 180
180/n + W = 180
W = 180 - 180/n = 180(1 - 1/n)

Answer 2

Oops.

720/n + W = 180
W = 180(1 - 4/n)

for n > 4

The postulated conditions do not hold for n = 3 or 4.

Answer 3

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