Given: An [tex]$n$[/tex]-gon

Prove: The sum of the measures of the interior angles is [tex]$180(n-2)^{\circ}$[/tex].

Complete the missing parts of the paragraph proof.

We are given an [tex]$n$[/tex]-gon, which has [tex]$n$[/tex] sides and [tex]$n$[/tex] vertices. If we choose one of the vertices, we can draw [tex]$(n-3)$[/tex] diagonals. These diagonals form [tex]$(n-2)$[/tex] triangles. The sum of the interior angle measures of a triangle is [tex]$180$[/tex] degrees. Therefore, [tex]$n-2$[/tex] triangles would have an interior angle measure sum of [tex]$180(n-2)$[/tex] degrees. Therefore, the sum of the measures of the interior angles of an [tex]$n$[/tex]-gon is [tex]$180(n-2)^{\circ}$[/tex].

Question

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24-07-2024
Mathematics

Answered

Given: An [tex]$n$[/tex]-gon

Prove: The sum of the measures of the interior angles is [tex]$180(n-2)^{\circ}$[/tex].

Complete the missing parts of the paragraph proof.

We are given an [tex]$n$[/tex]-gon, which has [tex]$n$[/tex] sides and [tex]$n$[/tex] vertices. If we choose one of the vertices, we can draw [tex]$(n-3)$[/tex] diagonals. These diagonals form [tex]$(n-2)$[/tex] triangles. The sum of the interior angle measures of a triangle is [tex]$180$[/tex] degrees. Therefore, [tex]$n-2$[/tex] triangles would have an interior angle measure sum of [tex]$180(n-2)$[/tex] degrees. Therefore, the sum of the measures of the interior angles of an [tex]$n$[/tex]-gon is [tex]$180(n-2)^{\circ}$[/tex].

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-24T15:18:49-04:00

We are given an [tex]$n$[/tex]-gon, which has [tex]$n$[/tex] sides and [tex]$n$[/tex] vertices. If we choose one of the vertices, we can draw [tex]$n - 3$[/tex] diagonals. These diagonals form [tex]$n - 2$[/tex] triangles. The sum of the interior angle measures of a triangle is 180 degrees. [tex]$n - 2$[/tex] triangles would have an interior angle measure sum of [tex]$180(n-2)$[/tex]. Therefore, the sum of the measures of the interior angles of an [tex]$n$[/tex]-gon is [tex]$180(n-2)^{\circ}$[/tex].