Polygon is a closed, connected shape do of straight lines. It may be a flat or a plane figure spanned throughout two-dimensions. A polygon is an enclosed number that have the right to have much more than 3 sides. The lines forming the polygon are well-known as the edges or sides and the points whereby they accomplish are recognized as vertices. The sides the share a common vertex among them are well-known as nearby sides. The edge enclosed within the surrounding side is dubbed the interior angle and also the external angle is referred to as the exterior angle.

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Exterior Angle

An exterior angle usually is formed by the intersection of any of the political parties of a polygon and extension of the nearby side the the chosen side. Interior and also exterior angles created within a pair of surrounding sides form a complete 180 degrees angle.Exterior-Angles-4

Measures the Exterior Angles

They are created on the outer part, the is, the exterior of the angle.The equivalent sum of the exterior and also interior angle developed on the very same side = 180°.The amount of every the exterior angles of the polygon is elevation of the variety of sides and is equal to 360 degrees, due to the fact that it bring away one complete turn to cover polygon in either clockwise or anti-clockwise direction.If we have a continual polygon that n sides, the measure of each exterior angle= (Sum of all exterior angles of polygon)/n= (360 degree)/nExterior-Angles-3


Theorem for Exterior Angles amount of a Polygon

If we observe a convex polygon, then the amount of the exterior angle current at every vertex will certainly be 360°. Following Theorem will describe the exterior angle sum of a polygon:

Proof

Let us consider a polygon which has n number of sides. The sum of the exterior angles is N.The sum of exterior angle of a polygon(N) =Difference between the amount of the direct pairs (180n) – the amount of the internal angles.(180(n – 2))N = 180n − 180(n – 2) N = 180n − 180n + 360N = 360 Hence, we have the amount of the exterior angle of a polygon is 360°.

Sample troubles on Exterior Angles

Example 1: find the exterior angle significant with x.Exterior-Angles-2


Solution:Since the amount of exterior angles is 360 degrees, the adhering to properties hold:∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 360°50° + 75° + 40° + 125° + x = 360°x = 360°Example 2: determine each exterior edge of the quadrilateral.Exterior-Angles-6Solution:Since, the is a continuous polygon, measure of each exterior angle= 360° number of sides= 360° 4= 90°Example 3: uncover the consistent polygon wherein each of the exterior edge is tantamount to 60 degrees.Solution:Since that is a constant polygon, the number of sides deserve to be calculated by the sum of every exterior angles, which is 360 degrees divided through the measure of every exterior angle.


Number of political parties = amount of all exterior angle of a polygon nValue of one pair of next = 360 degree 60 level = 6Therefore, this is a polygon enclosed in ~ 6 sides, the is hexagon.Example 4: find the internal angles ‘x, y’, and also exterior angles ‘w, z’ the this polygon?Exterior-AnglesSolution:Here we have ∠DAC = 110° the is one exterior angle and ∠ACB = 50° the is an interior angle.Firstly we have actually to find interior angle ‘x’ and also ‘y’.∠DAC + ∠x = 180° Linear pairs110° + ∠x = 180° ∠x = 180° – 110° ∠x = 70° Now,∠x + ∠y + ∠ACB = 180° Angle sum property of a triangle70°+ ∠y + 50° = 180° ∠y + 120° = 180°∠y = 180° – 120°∠y = 60°Secondly currently we can discover exterior angles ‘w’ and also ‘z’.∠w + ∠ACB = 180° Linear pairs∠w + 50° = 180°∠w = 180° – 50°∠w = 130°Now we can use the theorem exterior angles sum of a polygon,∠w + ∠z + ∠DAC = 360° Sum of exterior angle of a polygon is 360°130° + ∠z + 110° = 360°240° + ∠z = 360°∠z = 360° – 240°∠z = 120°
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