Question

the sides of a regular hexagon are produced in order prove that the sum of the exterior angles so formed is 4 right angles

Answer 1

Hey here is your Answer
=>

Suppose you have a ∆ABC
All the exterior angles will be equal to
(180-A)°
(180-B)°
(180-C)°
respectively (Angles on the same line) so if you sum it up it will be equal to 540 - (A+ B + C )
And by angle sum property A+B+C = 180°
Therefore Sum = 540 - 180 = 360.

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Answer 2

Answer:

We can solve this in 2 ways:
a)If we know that sum of exterior angles of any polygon is 360 degrees.(this is obviously easier)

b)If we don't know the above fact, we can do the following:

Step-by-step explanation:

Interior angle formula:180(n-2) where n=side

=>180(6-2)     (hexagon means 6 sides)

=>180*4

=720

the angle of each interior angle = 720/6

                                                     = 120 degrees.

=>the angle of each exterior angle = 180-120 (linear pair)

                                                          = 60 degrees.

=>exterior angle of hexagon = 60*6

                                                = 360 degrees.