4

Part of 2008 Swedish Mathematical Competition

Problems(1)

integer angles in convex polygon , whose degrees are divisible by 36

Source: 2008 Swedish Mathematical Competition p4

n

-side polygon has angles

v_1,v_2,\dots,v_n

(in degrees), where all

v_k

k = 1,2,\dots,n

) are positive integers divisible by

36

. (a) Determine the largest

n

for which this is possible. (b) Show that if

n>5

, two of the sides of the

n

-polygon must be parallel.

anglesgeometrycombinatorial geometry