Question

How many sides does a regular polygon have if the measure of an exterior angle is i) 400 ii) 450​

Answer 1

Answer:

The exterior angles of any regular polygon must add up to

360 degree

Since the angle measure given iin the questions s

40 degree

, take

360 degree

40o

= 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.