How many times is the sum of the interior angles of a convex dodecagon greater than the sum

| September 16, 2021 | education

How many times is the sum of the interior angles of a convex dodecagon greater than the sum of the interior angles of a convex hexagon?

Let us prove that the sum of the interior angles of a convex N-gon is 180 ° * (N – 2).

Choose any vertex of the N-gon and connect it by segments with all other vertices,

except for the neighboring ones. We obtain a partition of the N-gon into (N – 2) triangles, the sum of the angles of which coincides with the sum of the interior angles of the N-gon.

Therefore, the sum of the interior angles of a convex N-gon is 180 ° * (N – 2).

Then the sum of the interior angles of a convex dodecagon is

180 ° * (12 – 2) = 1800 °.

And the sum of the interior angles of a convex hexagon is 180 ° * (6 – 2) = 720 °.

Therefore, the sum of the interior angles of a convex dodecagon is greater than the sum of the interior angles of a convex hexagon

1800/720 = 2.5 times.



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