Question

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class:
polygon/ quadrilateral quiz

1. write the equation used to solve for the sum of the interior angles of a polygon.
2. what is the sum of the exterior angles of a polygon?

Explanation:

1.

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

The formula to find the sum of the interior angles of a polygon with \( n \) sides (where \( n \geq 3 \) and \( n \) is an integer) is based on the fact that we can divide a polygon into \( (n - 2) \) triangles, and the sum of the interior angles of a triangle is \( 180^\circ \). So the formula is \( S=(n - 2)\times180^\circ \), where \( S \) is the sum of the interior angles and \( n \) is the number of sides of the polygon.

For any convex polygon (and even for non - convex polygons, when considering the exterior angles taken one at each vertex), the sum of the exterior angles is always a constant. When we walk around the polygon, turning by the exterior angle at each vertex, we complete a full circle. A full circle is \( 360^\circ \). So, regardless of the number of sides \( n \) (for \( n\geq3 \)) of the polygon, the sum of its exterior angles (one at each vertex) is \( 360^\circ \).

Answer:

The equation used to solve for the sum of the interior angles of a polygon is \( S=(n - 2)\times180^\circ \) (where \( S \) represents the sum of interior angles and \( n \) represents the number of sides of the polygon).

2.