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About Sum of Exterior Angles Formula
Let us first define an outside angle before learning the sum of exterior angles formula. A polygon's exterior angle is the angle formed by a side and its adjacent extended side. Observe the outer angles of the triangle below to understand this well. Sum of all exterior angles in any of the polygon is 360 degrees, according to the sum of external angle formula.
- ( Y + R = 180°). Y = 180° - R.
- Y + R + Y + R + R + Y = 180° + 180° + 180°
- 3R + 3Y = 540°
- 180° = R + R + R
- 180°= 3R
- Substituting this in above equation:
- 540° = 3Y + 180°
- 540° - 180° = 3Y
- 360° = 3Y
Therefore the Sum of the exterior angles = 360°
As a result, the sum of a triangle's outer angles equals 360°. We can also show that the total of all exterior angles of any polygon is 360 degrees. The total of outside angles can so be calculated using the formula:
Sum of the exterior angles of any polygon = 360°
Each exterior angle of the regular polygon of n sides = 360° / n.
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