Before going to know the sum of exterior angles formula, first, let us recall what is an exterior angle. An exterior angle of a polygon is the angle between a side and its adjacent extended side. This can be understood clearly by observing the exteriors angles in the below triangle. The sum of exterior angles formula says the sum of all exterior angles in any polygon is 360°.
What Is the Sum of Exterior Angles Formula?
From the above triangle, the exterior angles Y and R make up a linear pair.( Y + R = 180°). And this gives, Y = 180° - R.
Sum of all three exterior angles of the triangle:
Y + R + Y + R + Y + R = 180° + 180° + 180°
3Y + 3R = 540°
Sum of interior angles of a triangle:
R + R + R = 180°
3R = 180°.
Substituting this in the above equation:
3Y + 180° = 540°
3Y = 540° - 180°
3Y = 360°
Therefore the Sum of exterior angles = 360°
Thus, the sum of all exterior angles of a triangle is 360°. In the same way, we can prove that the sum of all exterior angles of any polygon is 360°. Thus, the sum of exterior angles can be obtained from the following formula:
Sum of exterior angles of any polygon = 360°
Each exterior angle of a regular polygon of n sides = 360° / n.
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