The sum of the interior angles of polygon is 1800. Find the number of sides in the polygon and, what do you call that polygon?
for n sides
exterior angle = 360/n
so interior angle = 180 - 360/n
sum of interior angles = n(180 - 360/n)
=180 n (1 - 2/n)
so here
1800 = 180 n (1 - 2/n)
10 = n - 2
n = 12 sides
duodecaon etc.:
http://www.absorblearning.com/mathematics/demo/units/KCA008.html
duodecagon I mean
You wrong
glooks
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To find the number of sides in a polygon and determine the name of the polygon, we can use the formula for the sum of the interior angles of a polygon.
The formula to find the sum of the interior angles of a polygon is given by:
Sum = (n - 2) * 180
where n represents the number of sides of the polygon.
In this case, we are given that the sum of the interior angles is 1800. So we can set up an equation:
1800 = (n - 2) * 180
Now, let's solve this equation to find the value of n, which represents the number of sides.
First, divide both sides of the equation by 180:
1800/180 = (n - 2)
Simplifying further:
10 = n - 2
Next, isolate n by adding 2 to both sides:
10 + 2 = n
12 = n
Therefore, the number of sides in the polygon is 12.
Now, let's determine the name of the polygon based on the number of sides. A polygon with 12 sides is called a dodecagon.
So, the answer is that the polygon with a sum of interior angles of 1800 is a dodecagon.