What is the name of a polygon if the ratio of the interior to exterior angle is 7:2?

1 Answer
Jan 10, 2017

It is a nonagon.

Explanation:

It is assumed that it is a regular polygon and ratio of 7:2 is between each pair of interior to exterior angle. As sum of the two angles is 180^@,

and each interior angle is 7/9xx180^@=140^@ and each exterior angle is 2/9xx180^@=40^@

As sum of all exterior angles is 360^@, total number of sides must be 360^@/40^@=9 and polygon is nonagon.

If it is not a regular polygon, 7:2 ratio must be between sum of all interior angles and sum of all interior angles.

Hence as sum of exterior angle is always 360^@, sum of interior angles is 360^@xx7/2=1260^@ and as sum of interior angles of a polygon with n sides is (n-2)xx180^@, we have

(n-2)xx180^@=1260^@ and n-2=1260^@/180^@=7

and n=7+2=9 and polygon is a nonagon.