Let's do this question, or a regular polygon with nine diagonals find the internal angle and external
angle was the video.
Give it a try and then let's do it together.
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I hope you've given it a try.
Let's do it together.
Say, in is the number of sites of the polygon.
Now, we are given that the number of diagonals is equal to nine, we have NC to minus in is equal to
nine C permutation and combination S..
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All right.
What does NC do?
That's in the end minus one by two and that minus in gives you nine.
Now instead of forming a quadratic equation and solving four nine, it's faster if you just do trial
and error.
Right.
So let's do a few trial and error operations.
Let's take in as ten.
In that case, what would be this?
This is in in nine.
Right.
That's ten in the nine divided by two minus ten almost.
Do you get that.
Forty five minus ten which is equal to thirty five.
So if anything the number of diagonals is 35, but we have only nine diagonals so it has to be less
than ten.
Right.
So let's take and is equal to seven.
What do we get in this case.
If any is equal to seven, you will see that you will get the answer as 14, right?
What is that, seven into six by two minus seven.
Over here you have twenty one minus seven, which is 14.
So that again is greater than nine.
So let's try and is equal to six.
In that case, it would be six in the five by two minus six.
So you get 15 minus six which is equal to nine.
The N is equal to six, gives you nine diagonals.
Therefore the number of sides of this polygon is equal to six.
So we are dealing with the hexagon already.
Now what is the sum of internal angles of a polygon?
It's in minus two in two 180 right now because it's a regular polygon.
What would be each internal angle?
It is in minus two into 180 divided by in.
Now let's apply and is equal to six over here.
Will we get four into 180 divided by six.
Right.
That is equal to 120.
Therefore, the internal angle of this polygon is equal to 120 degree.
Now we know that the internal and external angle of the polygon are supplementary.
That is, they add up to 180 degrees.
Therefore, the external angle is equal to 180 minus 120, which is equal to 60 degrees.