In Spanish, what is the appropriate word for a convex polygon with a total of 1,080 degrees in its interior angles?

To determine the appropriate word for a convex polygon with a total of 1,080 degrees in its interior angles, we can use the formula for the sum of the interior angles of a polygon, which is given by:

[ S = (n - 2) \times 180 ]

where ( S ) is the sum of the interior angles and ( n ) is the number of sides (or edges) of the polygon.

In this case, we need to set the sum equal to 1,080 degrees:

[ 1,080 = (n - 2) \times 180 ]

Solving for ( n ):

1. Divide both sides by 180:

[ \frac{1,080}{180} = n - 2 ]

[ 6 = n - 2 ]

2. Add 2 to both sides:

[ n = 6 + 2 = 8 ]

This indicates that the polygon has 8 sides. In Spanish, a polygon with 8 sides is called "octágono."

Thus, the correct answer, which corresponds to a convex polygon with interior angles summing to 1,080 degrees, is "oct