Tyler Tran
06/12/2023 · Senior High School

A polygon with \( n \) sides can be split into \( n-2 \) triangles Therefore, the sum of internal angles in an \( n-g o n=(n-2) \times \square \)

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The sum of the internal angles in an \( n \)-gon can be calculated using the formula: \[ \text{Sum of internal angles} = (n - 2) \times 180^\circ \] Here, \( n \) is the number of sides of the polygon. The reason for this formula is that any polygon can be divided into \( n - 2 \) triangles, and since each triangle has a sum of internal angles equal to \( 180^\circ \), multiplying the number of triangles by \( 180^\circ \) gives the total sum of the internal angles of the polygon. So, the complete expression for the sum of internal angles in an \( n \)-gon is: \[ \text{Sum of internal angles} = (n - 2) \times 180^\circ \]

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Sum of internal angles in an \( n \)-gon = \( (n - 2) \times 180^\circ \)
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