What is the formula for a single interior angle of a regular polygon with n sides?

What is the formula for a single interior angle of a regular polygon with n sides?

• A. (180(n+2))/n
• B. (180(n-2))/n
• C. (180(n-2))/2
• D. (360/n)

Answer: (C)

To find the formula for a single interior angle of a regular polygon with \( n \) sides, we first need to understand the relationship between the number of sides and the interior angles. The sum of the interior angles of a polygon is given by the formula \( 180(n-2) \), where \( n \) is the number of sides. This formula arises because any polygon can be divided into \( n-2 \) triangles, and each triangle has a sum of interior angles equal to \( 180 \) degrees. Therefore, the total sum of the angles in the polygon is the number of triangles multiplied by \( 180 \). To find the measure of a single interior angle in a regular polygon, which has all its angles equal, you divide the total sum of the interior angles by the number of sides \( n \): \[ \text{Interior angle} = \frac{180(n-2)}{n} \] This is why the correct formula for a single interior angle of a regular polygon is given by \( (180(n-2))/n \). This choice correctly represents the relationship between the number of sides in the polygon and the measures of its interior angles, leading to a clear understanding of how these

To find the formula for a single interior angle of a regular polygon with ( n ) sides, we first need to understand the relationship between the number of sides and the interior angles.

The sum of the interior angles of a polygon is given by the formula ( 180(n-2) ), where ( n ) is the number of sides. This formula arises because any polygon can be divided into ( n-2 ) triangles, and each triangle has a sum of interior angles equal to ( 180 ) degrees. Therefore, the total sum of the angles in the polygon is the number of triangles multiplied by ( 180 ).

To find the measure of a single interior angle in a regular polygon, which has all its angles equal, you divide the total sum of the interior angles by the number of sides ( n ):

[

\text{Interior angle} = \frac{180(n-2)}{n}

]

This is why the correct formula for a single interior angle of a regular polygon is given by ( (180(n-2))/n ).

This choice correctly represents the relationship between the number of sides in the polygon and the measures of its interior angles, leading to a clear understanding of how these