Exterior angle of a polygon are formed when by one of its side and extending the various other side. The sum of every the exterior angles in a polygon is equal to 360 degrees. Friend are currently aware of the term polygon. A polygon is a flat figure that is made up of 3 or much more line segments and is enclosed. The line segments are referred to as the sides and also the allude where 2 sides satisfy is called the crest of the polygon. The pair of political parties that accomplish at the exact same vertex space called adjacent sides. An angle at one of the vertices is referred to as the interior angle. The internal and also exterior angle at each vertex varies because that all types of polygons. Now, permit us learn 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 formed by among the sides of any closed shape structure such as polygon and also the extension of its nearby side. See the figure below, wherein a five-sided polygon or pentagon is having actually 5 vertexes. The exterior angles of this pentagon are created by prolonging its surrounding sides.
Note: Exterior angle of a consistent polygon space equal in measure.
Sum that the Exterior angle of a Polygon
Let us say you start travelling native the peak at edge 1. You walk in a clockwise direction, do turns v angles 2, 3, 4 and 5 and come back to the same vertex. You spanned the whole perimeter of the polygon and also in fact, make one finish turn in the process. One finish turn is equal to 360 degrees. Thus, it have the right to be stated that ∠1, ∠2, ∠3, ∠4 and ∠5 sum up to 360 degrees.
Hence, the amount of the steps of the exterior angles of a polygon is same to 360 degrees, regardless of whether of the number of sides in the polygons.
Polygon Exterior Angle amount Theorem
If a polygon is a convex polygon, then the sum of its exterior angles (one at each vertex) is equal to 360 degrees. Let us prove this theorem:
Proof: consider a polygon v n variety of sides or one n-gon. The sum of that is exterior angle is N.
For any kind of closed structure, formed by sides and vertex, the sum of the exterior angle is always equal to the sum of straight pairs and sum of interior angles. Therefore,
N = 180n – 180(n-2)
N = 180n – 180n + 360
N = 360
Hence, we obtained the sum of exterior angle of n vertex equal to 360 degrees.
Exterior angle Examples
Example 1: In the given figure, discover the worth of x.
Solution: We recognize that the amount 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 kind of continuous polygon who exterior angle steps 120 degrees.
Solution: since the polygon is regular, the measure up of all the inner angles is the same. Therefore, every its exterior angles measure the same as well, the is, 120 degrees.
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Since the amount of exterior angles is 360 degrees and each one measures 120 degrees, us have,
Number of angles = 360/120 = 3
Since the polygon has actually 3 exterior angles, it has 3 sides. Hence it is an equilateral triangle.