If the exterior angle in a polygon is 12 degrees what is the number of sides?

Question

Violet Aldrich · Accepted Answer

May be #30# sides, but you need additional information.

You cannot find with the given information. The reason is that the only that is sure is that sum of all exterior angles of any polygon is always #360^@#. As one angle is #12^@#, only thing you can say is that sum of remaining angles is #360^@-12^@=348^@#. You do not know about other angles and number of sides could be any number. For example, if other angles are #1^@# each, we may have #349# sides (this means #348# angles of #1^@# and one of #12^@#) and if each off other angle is #6^@#, number of sides could be #59# (this means #58# angles of #6^@# and one of #12^@#). However, if we have added information that the polygon is a regular polygon , this means all interior as well as exterior angles would be equal. Then number of sides then would be #(360^@)/(12^@)=30#.

Violet Aldrich · Answer

undefined To find the number of sides in a polygon given the measure of one exterior angle, you can use the formula:

Number of sides = 360° / Measure of one exterior angle

In this case, the measure of one exterior angle is given as 12 degrees.

Number of sides = 360° / 12°

Number of sides = 30

So, the polygon has 30 sides.