Exterior angles of the polygon

Geometry is a branch of mathematics that studies the shapes, angles, dimensions, and sizes of a wide variety of everyday things. Geometry is made up of two Ancient Greek words: ‘geo,’ which means ‘Earth,’ and ’metron,’ which means ‘measurement.’ Euclidean geometry distinguishes between two- and three-dimensional shapes.

Triangles, squares, rectangles, and circles are examples of flat shapes in plane geometry. In solid geometry, solids are 3D shapes like the cube, cuboid, cone, and others. Points, lines, and planes are utilised in fundamental geometry, and coordinate geometry explains how they are used.

The various geometrical forms of shapes assist us all in comprehending the shapes we encountered in our day-to-day life. We can determine the area, perimeter, and volume using geometric concepts.

Polygon:-

A polygon is a two-dimensional geometric figure having a finite number of sides. The sides of a polygon are built up of end-to-end straight line segments. As a result, the line segments of a polygon are referred to as sides or edges. The vertex or corner is formed by the intersection of two line segments, and an angle is formed as a result. A polygon is a shape with three sides, such as a triangle. Because it is curved and lacking sides and angles, a circle is not considered a polygon, even if it is a plane figure. As a result, while all polygons are two-dimensional shapes, not all two-dimensional figures are polygons.

Definition:-

The outer angles of a polygon are created by extending one of its sides and extending the other. 360 degrees is the sum of all the outside angles in a polygon. You’ve probably heard of the phrase “polygon.” A polygon is a flat shape that is contained and made up of three or more line segments. The sides of the polygon are the line segments, and the vertex is the point where two sides meet. Adjacent sides are a pair of sides that meet at the same vertex. The inner angle is the angle formed by one of the vertices. All forms of polygons have different internal and exterior angles at each vertex. An exterior angle is generated by one of the sides of a closed shape construction, such as a polygon, and the extension of the neighbouring side. A five-sided polygon or pentagon has five vertices. Extending the adjacent sides of this pentagon produces its outside angles.

• They are formed on the polygon’s outside or outside.
• Because they are on the same straight line, the sum of an internal angle and its matching exterior angle is always 180 degrees.

Sum of the Exterior Angles:-

Assume you begin your journey at angle 1 from the vertex. You turn clockwise, passing through angles 2, 3, 4, and 5, before returning to the same vertex. You covered the entire perimeter of the polygon and, in the process, completed one complete round. 360° equals one complete turn. As a result, the total of ∠1, ∠2, ∠3, ∠4 and ∠5 equals 360° .

As a result, regardless of the number of sides in the polygons, the sum of the measures of the outside angles equals 360 degrees.

Polygon Exterior Angle Sum Theorem:-

The total of a convex polygon’s exterior angles (one at each vertex) equals 360 degrees. Let’s put this theorem to the test:

Consider a polygon with n sides, sometimes known as an n-gon. Its outer angles add up to N.

The sum of exterior angles is always equal to the total of linear pairs and sum of interior angles for every closed structure formed by sides and vertices. Therefore,

             N = 180°n – 180°(n-2)

             N = 180°n – 180°n + 360°

             N = 360°

As a result, the sum of n vertex’s outside angles equals 360° .

Exterior angle of a 9-sided regular polygon:-

For a 9-sided polygon, the number of exterior angles should be 9 .

And also we know that, the sum of all exterior angles of any polygon add to 360°

As it is a regular polygon, every external angle must be the same.

Thus measure of each angle would be equal to = 360°/9 = 40°

Conclusion:-

A side and an extension of a neighbouring side form an external angle in a polygon. A polygon’s outside angles have various distinct features. The sum of a polygon’s outside angles is always 360 degrees. As a result, measure of each exterior angle for all equiangular polygons equals 360° divided by the number of sides in that polygon.