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What is the measure of an exterior angle of a dodecagon?

2 Answers
Dec 6, 2015

Answer:

Exterior angles of dodecagon measure #30^o#.

Explanation:

Exterior angle of a dodecagon (12-sided regular polygon) is supplementary to its interior angle.

Sum of all interior angles of #N#-sided regular polygon equals to
#(N-2)*180^o#.
Therefore, sum of interior angles of #12#-sided polygon is
#(12-2)*180^o=1800^o#

All 12 interior angles of dodecagon are equal, so each is
#1800^o/12=150^o#

A supplementary exterior angle, therefore, equals to
#180^o-150^o=30^o#

Dec 6, 2015

Answer:

#30˚#

Explanation:

For a regular #n#-gon, the measure of an exterior angle is #(360˚)/n#.

Since a dodecagon has #12# sides, an exterior angles is #(360˚)/12=30˚#.