Answered

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2. The sum of the measures of the interior angles of a polygon is equal to [tex]$180(n-2)$[/tex], where [tex]$n$[/tex] is the number of sides of the polygon. What is the sum of the measures of the interior angles of a polygon with twelve sides?

A) [tex]$1,080^{\circ}$[/tex]
B) [tex][tex]$1,800^{\circ}$[/tex][/tex]
C) [tex]$2,160^{\circ}$[/tex]
D) [tex]$2,520^{\circ}$[/tex]

Sagot :

GinnyAnsweridn
To solve for the sum of the measures of the interior angles of a polygon with twelve sides, we can use the given formula:

[tex]\[ \text{Sum of interior angles} = 180(n-2) \][/tex]

Here, [tex]\( n \)[/tex] represents the number of sides of the polygon. Since we are considering a polygon with twelve sides, we have:

[tex]\[ n = 12 \][/tex]

Now, substitute [tex]\( n = 12 \)[/tex] into the formula:

[tex]\[ \text{Sum of interior angles} = 180(12-2) \][/tex]

Simplify the expression inside the parentheses first:

[tex]\[ 12 - 2 = 10 \][/tex]

Then, multiply 180 by 10:

[tex]\[ 180 \times 10 = 1800 \][/tex]

So, the sum of the measures of the interior angles of a polygon with twelve sides is:

[tex]\[ 1800^{\circ} \][/tex]

Therefore, the correct answer is:

B) [tex]\( 1,800^{\circ} \)[/tex]
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