Fig. 6 Regular pentagon
Since l\m, the corresponding angles, ZOAB and
ZFOH have the same size as do the alternate interior
angles, ZABO and ZBOH. Since the three angles, ZAOB,
ZBOH, and ZFOH sum to 180°, a = 180 - 2ß, and since
the exterior angle, ZCBG, also has that size, the central
angle and exterior angle both have the size of 360°/n.
These arguments work for any regular w-gon (w > 3)
(Fig. 7, where the regular n-gon is not complete).
180 -2ß
Fig. 7