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

It is a nonagon.

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.