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

1 Answer
Jan 10, 2017

Answer:

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.