Question

exterior angle property of triangle,quadrilateral,pentagon

Answer 1

An exterior angle of a triangle is equal to the sum of the opposite interiorangles. For more on this see Triangleexternal angle theorem. If the equivalent angle is taken at each vertex, the exterior angles always add to 360

for quadrilateral

the sum of the angles in a triangle = 180° to prove that the angle sum of aquadrilateral is 360°.

for Pentagon

for all equiangular polygons, the measure of one exterior angle is equal to 360 

Answer 2

The exterior angle of a polygon and its corresponding interior angle always add up to 180° (because they make a straight line). For any polygon, the sum of its exterior angles is 360°. You can see this because if you imagine 'walking' all the way round the outside of a polygon you make one full turn.

Conjecture (Exterior Angle Conjecture ): The sum of the n exterior angles for any convex polygon with n sides is 360 degrees. ... Explanation of the Corollary: There are n exterior angles, each with the same measure, and which add up to 360 degrees. Therefore, each of them must have measure equal to 360 divided by n.

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Hope this helps...