Before going to understand the sum of exterior angle formula, first, let us recall what is an exterior angle. An exterior edge of a polygon is the angle between a side and its adjacent extended side. This have the right to be understood clearly by observing the exteriors angle in the listed below triangle. The amount of exterior angle formula says the amount of every exterior angle in any polygon is 360°.
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What Is the sum of Exterior angles Formula?
From the over triangle, the exterior angles Y and R comprise a linear pair.(Y + R = 180°). And also this gives, Y = 180° - R.
Sum that all 3 exterior angles of the triangle:Y + R + Y + R + Y + R= 180° +180° +180°3Y + 3R = 540°
Sum of inner angles that a triangle:R + R + R =180°3R =180°.
Substituting this in the above equation:3Y + 180° = 540°3Y = 540° - 180°3Y = 360°
Therefore the amount of exterior angles = 360°
Thus, the sum of all exterior angles of a triangle is 360°. In the exact same way, we can prove the the sum of all exterior angle of any polygon is 360°. Thus, the sum of exterior angles have the right to be obtained from the adhering to formula:
Sum the exterior angles of any type of polygon = 360°
Each exterior edge of a continuous polygon of n sides = 360° / n.
Let us inspect a couple of solved examples to learn more about the sum of exterior angles formula.
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Solved examples on sum of Exterior angle Formula
Example 1:Find the measure of each exterior edge of a constant hexagon.
To find: The measure up of every exterior angle of a continual hexagon.
We recognize that the variety of sides that a hexagon is, n = 6.
By the sum of exterior angle formula,
Each exterior edge of a constant polygon the n sides = 360° / n.
Substitute n = 6 here:
Each exterior edge of a hexagon = 360° / 6 = 60°
Answer: each exterior angle of a constant hexagon = 60°.
Example 2:Use the amount of exterior angles formula come prove the each internal angle and also its matching exterior edge in any polygon aresupplementary.
To prove: The amount of an inner angle and also its matching exterior angle is 180°.
Let us consider a polygon that n sides.
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By the sum of exterior angles formula,
Sum the exterior angle of any type of polygon = 360°
By the sum of internal angles formula,
Sum of inner angles of any type of polygon = 180 (n - 2)°
By including the over two equations, we gain the amount of all n inner angles and also the sum of all n exterior angles:
360° + 180 (n - 2)° = 360° + 180n - 360° = 180n
So the amount of one interior angle and also its equivalent exterior edge is:
180n / n = 180°
Answer: An interior angle and its corresponding exterior angle in any polygon room supplementary.