Question

the sum of the interior angles of an n-gon is ______.
90°(n - 2)
270°(n - 2)
180°(n - 2)
360°(n - 2)

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of the interior angles of an \( n \)-sided polygon (n - gon) is derived by dividing the polygon into \( (n - 2) \) triangles. Since the sum of the interior angles of a triangle is \( 180^{\circ} \), the sum of the interior angles of an \( n \)-gon is \( 180^{\circ}(n - 2) \).

Step2: Match with the given options

Looking at the options, the correct formula is \( 180^{\circ}(n - 2) \).

Answer:

\( 180^{\circ}(n - 2) \) (the option corresponding to this formula)