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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