A regular polygon is a polygon that is equiangular, that is, all of the angles are equal in measure.

Let 'x' represent the inner angle and 'y' the outer angle.

x + y = 180

The ratio of the inner and outer angle is 7:2 means:

x : y = 7 : 2

7y = 2x

We have the following system of equations:

x + y = 180

7y = 2x

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click here to see the system of equations solved for x and y

........

x = 140 degrees

y = 40 degrees

Outer angle is 40 degrees and also

outer angle = 360/number of sides

number of sides = 360/outer angle

number of sides = 360/40

number of sides = 9

Each inner angle is 140 degrees.

Each outer angle is 40 degrees.

The polygon has 9 sides.