Question

18.How many sides does a regular polygon have if measure of an exterior angle is 40 degree?
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Answer 1

The exterior angles of any regular polygon must add up to 360o.

Since the angle measure given iin the questions s 40o, take 360o40o = 9. Meaning there are 9 exterior angles and therefore 9 sides to the polygon.



A regular polygon refers to a multi-sided convex figure where all sides are equal in length and all angles have equal degree measures.





The regular triangle has 3 interior angles of 60o and 3 exterior angles of 120o. The exterior angle have a sum of 360o =(3)120o

The square has 4 interior angles of 90o and 4 exterior angles of 90o. The exterior angle have a sum of 360o =(4)90o.

The square has 5 interior angles of 108o and 5 exterior angles of 72o. The exterior angle have a sum of 360o =(5)72o.

In order to find the value of the interior angle of a regular polygon the equation is (n−2)180n where n is the number of sides of the regular polygon.

Triangle (3−2)1803=60o

Square (4−2)1804=90o

Pentagon (5−2)1805=72o

Finally

The interior and exterior angles of a regular polygon form a linear pair and therefore are supplementary and must add up to 180o.

Step-by-step explanation:

A regular polygon with exterior angles of 40o would have 9 side and be a nonagon.

Answer 2

Step-by-step explanation:

9 sides

measure of each angle = {(n-2)*180}/(n)

here,,, exterior angle = 40degree,

so ,, interior angle = 140degree

So 140= {(n-2)*180}/n give 140n =(n*180)- (2*180)

140n = 180n -360

180n -140n -360=0

40n -360= 0

40n = 360

n =360/40

n = 9sides