Question

What is the sum of the

Answer 1

Answer:

360 degree

Step-by-step explanation:

The sum of all the exterior angles is 360 for any polygon.

This can be proved for polygon with 20 sides also.

We know that sum of all the angles of polygon is given by formula = (2*n -4) *90

where n is the no. of sides of polygon

for 20 sides polygon sum of  sum of all the angles = (2*20 -4) * 90

= (40-4)*90 = 36*90 = 3240 degree

measure of each angle of polygon = sum of total angles of polygon/ no of sides of polygon = 3240/20 = 162

We also know that sum of interior and exterior angle of triangle is 180 degree, as interior and exterior angle  lies on straight line and they  are supplementary

so

162 + value of exterior angle = 180

=> value of exterior angle = 180 - 162 = 18

Value of one exterior angle is 18 degree

in 20 sided polygon there are 20 exterior angle

therefore, value of 20 exterior angle is 18*20 degree which is 360 degree.

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As a general point one can memorize than sum of all the exterior angle for a polygon with any number of side is 360.