In this video, let's discuss these some of the exterior angles of a polygon.
Now, over here we have a hexagon.
It's a six sided polygon.
Let's mark the exterior angles taken in a particular direction.
So I extend right.
And I get this accident angle over here.
Similarly, I extend KBE in this direction to get angle three over here.
I extend back in this direction to get angle to over here.
I extend A.F. in this direction to get angle one over here, I extend F e in this direction to get angle
six over here and I extend it in this direction to get angle five over here.
So I have extended the sights taken in a particular direction.
Right.
And I have got six exterior angles.
All right.
Let's now find the some of angle, one angle, two, three, four, five, plus six.
Let's first see it visually.
If I take these angles and put them together around the point, you will see that it makes a complete
revolution.
And we know that a complete revolution is equal to 360 degrees.
So visually, we have seen that when we added these six angles, which were the six exterior angles
formed when we made exterior angles taken in a particular direction, the sum of those angles is equal
to 360 degrees.
Now, let's think of this in a different manner.
Let's think that a person is standing over here and he is facing this direction.
All right.
Let me start with this direction over here.
Now it turns by an angle for and moves in this direction till he reaches point C.
Now, after reaching buoyancy, he turns by an angle three and moves in this direction till point B.
Now, after reaching point B, he moves by an angle, too, and moves in this direction till point eight.
Then he turns by an angle one and moves in this direction till point F.
Now he would have moved again in this direction, right?
That's why he keeps turning.
After reading over here, he turns by an angle six and then he moves in this direction after reaching
point E, it moves by an angle five and then moves in this direction till he reaches back at point B
and he's looking in the same direction.
Right.
So you can see that if he started off in looking in this direction, he kept on rotating.
He kept on rotating.
And he came back looking in this direction, right?
So he has made one complete turn.
That's why the some of the external angles of a polygon is equal to 360 degrees.
Now, we have seen this before for a triangle.
Now over here we see that for any polygon, if you take the external angles in and order, the some
of the exterior angles is equal to 360 degrees.
Now, if the polygon is a regular polygon.
All the interior angles are equal, right, and all the exterior angles taken in an order will also
be equal.
In this case, where we have a regular polygon, each exterior angle is equal to 360, which is the
sum of the exterior angles divided by and which is the number of exterior angles.
Because if you have a six sided figure, you will have six exterior angles when you extend the sides
taken in an order already.
So over him, what would be each angle?
Because these are six figure.
Each angle is equal to 360 by six.
That's equal to 60 degrees.
So this angle over here is equal to 60 degrees.
This angle over here is equal to 60 degrees.
Given that hexagon, A, B, C, D, E, F is a regular hexagon.
All right.
Now, there is one more interesting thing that you can notice over here.
If you add the internal angle plus the external angle, you will get 180 degree Y because the internal
angle, which is this angle over here and the external angle form a linear pair.
And we have seen that when you have angles that form a linear pair, if you add them up, you will get
180 degrees.