If the sum of the interior angle measures of a polygon is 3600°, how many sides does the polygon have? A. 22 sides B. 20 sides C. 18 sides D. 10 sides

Respuesta :

Answer:

It is 22 not 10

Step-by-step explananation

Explanation: A polygon with interior angles totalling 3600∘ must be able to be divided into 20 triangles, by drawing diagonals from one vertex. If a figure can be divided into 20 triangles, it must have 22 sides. (The number of triangles is always 2 less than the number of sides.) To find this answer using the formula, set (n−2)⋅180=3600 and solve for n. First divide both sides by 180, yielding n−2=20. (This shows that the n-gon can be divided into 20 triangles.) Then add 2 to both sides to get n=22.