Question

Verify that the sum of measure of exterior angles of any polygon is 360 by paper cutting and pasting verify the results for (traingle (b) quadrilateral (c) Pentagon (d) hexagon

Answer 1

Answer:

Sum of All exterior angle of polygon = 360°

Step-by-step explanation:

A polygon have n sides  & n vertices

Now at each vertices Interior Angle + exterior angle = 180° ( straight line)

Sum of All  Interior Angle & exterior angle = n * 180°

Now i can draw n-2 triangles in a polygon starting from a point & completing all the vertices

Let say there are x1 , x2 , x3 ,..............................,xn-1 , xn  vertices

Δx1 , x2 x3 , Δx1 , x3 ,  x4  , Δx1 , x4 ,  x5            Δx1 , xn-2 xn-1  ,    Δx1 , xn-12 xn

Total n-2 triangles

Sum of interior angles of all these triangles = (n-2) * 180°

= Sum of interior Angles of polygon = (n-2) * 180°

(n-2) * 180° + Sum of All exterior angle of polygon = n * 180°

=> Sum of All exterior angle of polygon = 2 * 180°

=> Sum of All exterior angle of polygon = 360°

Answer 2

Answer:

sum of all exterior angle of polygon = 360

it will be help in the question