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

Did you know that the formula \( (n-2) \times 180^{\circ} \) is derived from the geometry of polygons? Each time you add a side to a polygon, you essentially add a triangle. Since the sum of angles in a triangle is \( 180^{\circ} \), multiplying the number of triangles (which is \( n-2 \), where \( n \) is the number of sides) gives you the total interior angle sum of the polygon! In practical terms, architects and designers use this formula all the time when planning spaces with multiple linear sections. For instance, if they need to design a 7-sided room (heptagon), they'd quickly calculate that the sum of the interior angles is \( (7-2) \times 180^{\circ} = 900^{\circ} \). This ensures their designs are not only functional but also maintain the beautiful symmetry that adds to the aesthetic appeal!