Let's do this question if the sides of a triangle are produced in an order so that the sum of the exterior
angles so formed is equal to 360 degree was the video, give it a thought and then let's do it together.
All right.
Over here, it's mentioned that the sides of the triangle are produced in an order to how can I do that?
I can produce them like this right this side over here.
I'm producing it like this.
This one I'm producing it like this and ebe and producing it like this.
Right.
What is the other way in which I could have produced them in an order.
I could have produced them in the opposite direction right over here instead of going towards the right.
I could have gone towards the left like this.
And then I should have produced this side in this manner and this side in this manner so I can take
any one of these two ways.
But the point mentioned in the question is the sites have to be produced in an order.
All right.
Let's move on.
Let me make some space over here.
Now, let me mark the three exterior angles so formed.
That's angle one angle to an angle trip and let's mark the three interior angles, that's angle four
and five and angle six.
Now we need to prove that angle one plus angle two plus angle three is equal to 360 degrees.
All right.
Now from the exterior angle property, we know angle one is equal to angle five plus angle six.
Right, because five and six are interior opposite angles for angle one.
Similarly, angle two is equal to angle for angle five and angle three will be equal to angle for angle
six.
All right.
Now let's add these three angles up to angle one plus angle two plus angle three is equal to angle five
plus six plus four plus five plus four plus six.
Now aggregating them, we get that as two times angle five plus six plus four.
Now as per the angle, some property of a triangle, we know that angle four plus five plus six is equal
to 180 degrees.
Therefore this is equal to two times 180 degrees, which is equal to 360 degree.
Now, we have seen that the sum of the exterior angles of a triangle taken in an order is equal to 360
degree.
Now, this is not only true for a triangle, it's true for any polygon.
If you take any polygon, whether it's a Pentagon or a quadrilateral or a hexagon to dig any quadrilateral
or polygon, and you add up the exterior angles, the sum of the angles so obtained will be equal to
360 degrees.
Now, there is an interesting way in which you can think about it.
Imagine a person is standing at Point C looking in this direction right now.
He turns by an angle to and starts walking in the direction.
See it till he reaches point A after reaching point A, he turns by an angle one and walks in the direction
Ebbie till he reaches point B.
After reaching point B, he turns by an angle tree and starts walking in the B C direction.
Dilli gets back to point C now a person started looking in this direction.
Now he keeps making rotations of Angle to.
Right, and afterwards and angle one.
Then angle three and finally he's back looking in the same direction, right?
So what is actually happening is he's doing one complete revolution and we know that one complete revolution
around the point is equal to 360 degrees.
That's why when you add all the exterior angles taken in an order, you get the Sonmez 360 degree.
And this is true for any polygon.