# The inner angle of a regular polygon is equal to a = 140 ° define the type of the polygon.

July 29, 2021 | education

| There is a known formula for determining the sum of the angles of a regular polygon:

S = 180 ° (n – 2), where n is the number of sides.

On the other hand, the internal angle is known to be 140 °, and we can express the sum of the angles as the product of the number of angles by the value of the internal angle:

S = n * 140 °.

We compose equality:

180 ° (n – 2) = n * 140 °.

Find the number of sides:

180 ° * n – 360 ° = n * 140 °;

40 ° * n = 360 °;

n = 9.

The number of sides is equal to the number of corners.

Answer. Regular hexagon.

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