Answer:
The correct answer is D. 360°
Step-by-step explanation:
The sum of all the exterior angles of a regular n-gon or a polygon is always equal to 360°.
Let us consider the image attached.
First of all let us consider the triangle.
As per the property of exterior angles: The exterior angle is equal to the sum of 2 opposite interior angles.
[tex]\Rightarrow \angle 1=\angle B + \angle C\\\Rightarrow \angle 2=\angle A + \angle C\\\Rightarrow \angle 3=\angle A + \angle B[/tex]
Where [tex]\angle A, \angle B\ and\ \angle C[/tex] are the interior angles of the triangle.
Adding the above equations:
[tex]\angle 1 +\angle 2 +\angle 3 = 2 \times (\angle A +\angle B +\angle C )[/tex]
The sum of interior angles of a triangle is always equal to 180°
[tex]\angle A +\angle B +\angle C = 180^\circ[/tex]
[tex]\angle 1 +\angle 2 +\angle 3 = 2 \times 180^\circ\\\Rightarrow \angle 1 +\angle 2 +\angle 3 = 360^\circ[/tex]
Hence, proved that the sum of exterior angles is [tex]360^\circ[/tex].
So, the correct answer is D. [tex]360^\circ[/tex]
