Question

polygon interior angles theorem\
polygon exterior angles theorem

Explanation:

The problem is about polygon angle theorems. The Polygon Interior Angles Theorem states that the sum of the interior angles of an \( n \)-sided polygon is \( (n - 2)\times180^\circ \). The Polygon Exterior Angles Theorem states that the sum of the exterior angles of any polygon (one at each vertex) is \( 360^\circ \). These are fundamental concepts in Geometry (a subfield of Mathematics) related to the properties of polygons.

Answer:

• Polygon Interior Angles Theorem: For a polygon with \( n \) sides, the sum of the interior angles \( S_{interior}=(n - 2)\times180^\circ \).
• Polygon Exterior Angles Theorem: The sum of the exterior angles of any polygon (taking one exterior angle at each vertex) is \( S_{exterior} = 360^\circ \).