How many sides does a convex polygon have if the sum of its angles is 2 times the sum of the angles of a convex 9 gon?

univerkov | July 3, 2021 | education

The sum of the angles of the polygon is: 180 ° (n – 2), where n is the number of sides of the polygon;

For a hexagon, the sum of the angles is 180 ° (9 – 2) = 1260 °;

The unknown polygon has a sum of angles: 1260 * 2 = 2520 °;

n – 2 = 2520 °: 180 °; n – 2 = 14; n = 14 +2;

n = 16.

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