Question

prove that the exterior angle of polygon is 360

Answer 1

From the centre of a polygon of n-sides (n-gon), draw rays towards the n-vertices thus forming n triangles.

The sum of internal angles of the n triangles equals 180n°. This sum also equals the sum of the n interior angles plus the angles around the central point, 360°. Call this sum A.

Extend each side of the n-gon to create an exterior angle. The sum of the exterior angle and the corresponding interior angle equals 180°. So the sum of all the exterior angles and interior angles of the n-gon equals 180n°. Call this sum B.

Since both equal 180n°,
sum A = sum B, or
360°+∑interior angles = ∑exterior angles + ∑ interior angles
Cancel out ∑interior angles, we get
∑exterior angles = 360°.