the sum of the measures of the interior angels of a convex polygon is 3240 classify the polygon by the number of sides
Mathematics · Middle School · Sun Jan 24 2021
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To classify the polygon by the number of sides based on the sum of the measures of the interior angles, we'll start by using the formula for the sum of the interior angles (S) of a polygon, which is given by:
S = (n - 2) × 180°
where n is the number of sides in the polygon.
You have been given that the sum of the interior angles of the polygon is 3240 degrees. We can set up the equation to solve for n:
3240° = (n - 2) × 180°
To find n, you need to divide both sides of the equation by 180°:
(3240°) / (180°) = n - 2
18 = n - 2
Now, add 2 to both sides to solve for n:
n = 18 + 2 n = 20
The polygon with the sum of the interior angles of 3240 degrees is therefore a polygon with 20 sides, which is called an icosagon.