To understand the formulas for finding the interior and exterior angles of a polygon, we first need to grasp the basic properties of polygons.
Interior Angles:
The sum of the interior angles of a polygon can be calculated using the formula:
Sum of Interior Angles = (n – 2) × 180°
where n is the number of sides in the polygon. For example, a triangle (3 sides) has a sum of interior angles equal to (3 – 2) × 180° = 180°, which aligns with our understanding that the angles in a triangle add up to 180°.
Exterior Angles:
The sum of the exterior angles of any polygon is always 360°, regardless of the number of sides. The exterior angle at each vertex can be found as follows:
Exterior Angle = 360° / n
Thus, for a regular polygon, where all sides and angles are equal, you can easily calculate each exterior angle. For instance, a square (4 sides) has each exterior angle equal to 360° / 4 = 90°.
To summarize:
– The formula for the sum of interior angles of a polygon is (n – 2) × 180°.
– The sum of the exterior angles of any polygon is always 360°.
– Each exterior angle for a regular polygon can be found using 360° / n.
Understanding these formulas can help you analyze and work with various polygons in geometry.