In this video, let's think about the gruesome property of a quadrilateral and then we will extend it
to the angles and property of a polygon.
All right, let's take an example.
We have quadrilateral ABCDE over here.
Now I need to find the sum of Angley plus angle B plus angle C plus angle D.
That's what we are trying to find out.
All right.
Let me join point E and buoyancy over here.
OK, so you can see that I'm getting two triangles over here right now, let me mark the angles of this
triangle, this angle one, this angle, two, three, four, five and six.
Now we are trying to find out angle E-Plus, angle B plus angle C plus angle D.
You can see visually that this is the same as angle one plus two plus three plus four plus five plus
six.
Right.
Two is equal to B itself and five is equal to the itself.
And you can see one plus four gives you a right.
So you have one and four and similarly three plus six gives you see.
So angle eight plus plus C plus these the same angle one plus two plus three plus four plus five plus.
All right.
Now we have learned before that the sum of the angles of a triangle is equal to 180 degrees.
Therefore one plus two plus three is equal to 180 degrees.
Right.
Similarly, you can see that four plus five plus six is also equal to 180 degree.
Therefore, angle A plus angle B plus angle C plus angle is equal to 360 degrees.
All right.
So the angle some of a what level is equal to 360 degrees.
Now let's keep this aside and generalize it for a polygon over here.
Let's analyze the relation between the number of sides and the angles.
We have seen that in the case where the number of sites is for the angle, sum is equal to two in the
180 or 360 degrees right now.
Why is it doing the 180?
Because when you have four sides, you are able to form two triangles.
That's why you have two into the sum of the angles of a triangle that is doing the 180, which gives
you 360.
All right.
Now, what would be the case if you have a five sided polygon?
In that case, the sum of the angles will be five minus two in the 180, which is three in the 180.
Let's see why that is.
So over here.
I have a Pentagon.
That's three sides, this is four sides, and I have five sites, so this is the Pentagon now that's
a five sided polygon, you can see that I can form.
Three triangles, one, two, three, three triangles, therefore the angles will be three and do 180,
and these three you get by doing five minus two.
So let's generalize it.
If you have an incited polygon, the angles will be equal to N minus two in two, 180 to four.
The case where the sides were four, we got four minus two.
That is true.
In the case of the Pentagon, it is five minus two.
That's three to 180.
All right.
Now let's try to find out what would be the measure of each internal angle.
Now, in the case where the polygon under consideration is a regular polygon, we can find that each
internal angle will be equal.
Therefore, as you have in internal angles, when you have inside, each internal angle will be in minus
two in the 180, divided by in.
Right.
This is the sum and each angle is equal.
So if the measure of each angle is X degrees and you have in angles and that is equal to minus two in
two 180, which is the sum.
Right.
Therefore X is equal to minus two by 180, divided by in each angle in a regular polygon will be of
the measure and minus two in two 180 divided by an.