Question

1. choose the correct answer. the polygon interior angle sum theorem states that the sum of the measures of the interior angles of a convex polygon with n sides is ____.

\\( \frac { n ^ { 2 } - 3 n } { 2 } \\)
\\( ( n - 2 ) 180 ^ { \circ } \\)
triangle sum theorem
\\( 180 ^ { \circ } \\)

Explanation:

Step1: Recall the Polygon Interior Angle Sum Theorem

The Polygon Interior Angle Sum Theorem is a well - known formula in geometry.
For a convex polygon with \(n\) sides, we can divide the polygon into \((n - 2)\) non - overlapping triangles.

Step2: Calculate the sum of interior angles

Since the sum of the interior angles of a triangle is \(180^{\circ}\).
If a convex polygon with \(n\) sides can be divided into \((n - 2)\) triangles, then the sum of the interior angles of the polygon \(S=(n - 2)\times180^{\circ}\)

Answer:

\((n - 2)180^{\circ}\)