Exterior angle of a polygon are developed when by one of its side and also extending the various other side. The amount of all the exterior angle in a polygon is equal to 360 degrees. Friend are already aware of the ax polygon. A polygon is a flat number that is consisted of of three or much more line segments and also is enclosed. The line segments are dubbed the sides and also the allude where two sides accomplish is called the peak of the polygon. The pair of political parties that accomplish at the very same vertex room called surrounding sides. An angle at among the vertices is called the internal angle. The internal and exterior angle at each vertex varies because that all species of polygons. Now, permit us discover in detail the ide of that is exterior angles.
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What room Exterior Angles?
An exterior edge is one angle which is developed by one of the political parties of any closed shape structure such as polygon and also the expansion of its adjacent side. View the figure below, whereby a five-sided polygon or pentagon is having 5 vertexes. The exterior angle of this pentagon are developed by prolonging its surrounding sides.
Note: Exterior angle of a constant polygon are equal in measure.
Sum the the Exterior angle of a Polygon
Let us say you begin travelling indigenous the peak at edge 1. You walk in a clockwise direction, do turns v angles 2, 3, 4 and also 5 and come ago to the exact same vertex. You extended the whole perimeter of the polygon and also in fact, make one complete turn in the process. One finish turn is same to 360 degrees. Thus, it can be said that ∠1, ∠2, ∠3, ∠4 and also ∠5 amount up to 360 degrees.
Hence, the amount of the procedures of the exterior angle of a polygon is equal to 360 degrees, regardless of of the number of sides in the polygons.
Polygon Exterior Angle amount Theorem
If a polygon is a convex polygon, climate the amount of that exterior angles (one at every vertex) is equal to 360 degrees. Let united state prove this theorem:
Proof: consider a polygon with n variety of sides or one n-gon. The sum of that is exterior angles is N.
For any kind of closed structure, developed by sides and also vertex, the amount of the exterior angle is constantly equal to the sum of straight pairs and sum of internal angles. Therefore,
N = 180n – 180(n-2)
N = 180n – 180n + 360
N = 360
Hence, we acquired the amount of exterior angle of n vertex same to 360 degrees.
Exterior angle Examples
Example 1: In the provided figure, find the value of x.
Solution: We recognize that the sum of exterior angle of a polygon is 360 degrees.
Thus, 70° + 60° + 65° + 40° + x = 360°
235° + x = 360°
X = 360° – 235° = 125°
Example 2: recognize the type of regular polygon who exterior angle steps 120 degrees.
Solution: because the polygon is regular, the measure of every the inner angles is the same. Therefore, every its exterior angle measure the same as well, the is, 120 degrees.
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Since the amount of exterior angle is 360 degrees and each one steps 120 degrees, us have,
Number of angles = 360/120 = 3
Since the polygon has actually 3 exterior angles, it has actually 3 sides. Thus it is one equilateral triangle.