Problem: The sides of a regular polygon of n sides, n>4, are extended to form a star. The number of degrees at each point of the star is:
Answer Choices:
A. n360
B. n(n−4)180
C. n(n−2)180
D. 180−n90
E. n180
Solution:
Each such angle is the vertex angle of an isosceles triangle whose base angles are each, in degrees, 180−(n−2)180/n=360/n.
∴ angle =180−(720/n)=(180n−720)/n=180(n−4)/n