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Find the sum of the interior angle measures of a 14-gon.
The sum is___ degrees.

1 Answer

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Explanation:

the sum of interior angles in a triangle is 180°.

the sum of interior angles of a polygon, is the product of the number of triangles in the polygon (that can be created from a single vertex or corner via lines to all other corners) and 180°.

so, in reality, the number of triangles in each polygon is two less than the number of sides (because the lines to the 2 neighboring corners are sides and do not create triangles).

so the formula for the sum of all interior angles is

(n - 2) × 180

with n being the number of sides of the polygon.

in our case

(14 - 2) × 180 = 12×180 = 2160°

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