Polygon Exterior Angle-sum Theorem description/definition
The Polygon Exterior Angle-sum Theorem states that the sum of the measures of the exterior angles of any polygon is equal to 360°. An exterior angle of a polygon is an angle formed by one side of the polygon and the extension of an adjacent side.
Haven't you beaten this type of problem to death yet? Surely by now you know how to solve them.
The Polygon Exterior Angle-Sum Theorem states that the sum of the measures of the exterior angles of any polygon is always 360 degrees.
An exterior angle of a polygon is formed by extending one of the sides of the polygon and the adjacent side. This creates an angle outside the polygon. The measure of this exterior angle is equal to the sum of the two non-adjacent interior angles of the polygon.
For example, consider a triangle. The sum of its exterior angles will always be 360 degrees. If we extend one side of the triangle, it forms an exterior angle. The measure of this exterior angle is equal to the sum of the two non-adjacent interior angles, which is equal to 180 degrees. Similarly, for a quadrilateral, the sum of its exterior angles will also be 360 degrees, and so on for any polygon.
This theorem can be useful when solving problems that involve finding the measures of angles in polygons or determining the number of sides in a polygon when given the measures of its exterior angles.
The Polygon Exterior Angle-sum Theorem states that the sum of the measures of the exterior angles of any polygon is always 360 degrees.
To understand this theorem, let's start by defining some key terms:
- A polygon is a closed figure made up of line segments called sides. Examples of polygons include triangles, quadrilaterals, pentagons, hexagons, and so on.
- An exterior angle is formed by extending one side of the polygon and the adjacent side.
The Polygon Exterior Angle-sum Theorem tells us that if we were to extend all the sides of a polygon and measure each exterior angle formed, the sum of these exterior angles would always be 360 degrees.
One way to prove this theorem is by considering the relationship between the interior angles and exterior angles of a polygon. For any polygon, the measure of each interior angle is given by the formula: (n-2) * 180, where n represents the number of sides of the polygon.
Now, when we extend a side of a polygon to form an exterior angle, we create a straight line with one of the interior angles adjacent to the exterior angle. Since the sum of the interior angles of a polygon is always (n-2) * 180 degrees, the exterior angle and the adjacent interior angle together form a straight line, which measures 180 degrees.
Therefore, the sum of the measures of all the exterior angles of a polygon can be found by multiplying the number of sides (n) by 180 degrees, which is equal to 360 degrees.
In summary, the Polygon Exterior Angle-sum Theorem states that the sum of the measures of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides it has.