Let's do this questions the Polyana in which some of all exterior angles is equal to the sum of the
interior angles is covered.
All right, pose the video, give it a try, and then let's do it together.
All right, let's do it together.
I hope you have given it a try.
Now, the sum of all exterior angles in a polygon we have seen is equal to 360 degree.
Right.
And what is the sum of interior angles if there are inside?
The sum of interior angles will be equal to and minus two in two 180.
Now, in this question, it's mentioned that these two are equal.
Let's solve four and we get that two is equal to and minus two or N is equal to four now and is equal
to four.
Is it quadrilateral.
Right to the sum of the exterior angles in a column is equal to 360 degree.
And we have seen that the sum of the interior angles inequality is equal to 360 degrees.
So the answer over here is quadrilateral.
All right, let's go to the next question.
Which of the following can never be the measure of the exterior angle of a regular polygon?
Was the video.
Give it a try and then let's do it together.
All right.
Let's do it together.
We know that in the case of a regular polygon, the exterior angle is equal to three sixty, divided
by N, right.
So therefore N is equal to 360, divided by the exterior angle now.
So it has to divide.
Exactly right.
Therefore, the answer to this question.
Is equal to option eight, that's 22, right?
Why is that so?
Why should it divide exactly?
If it does not divide exactly, you will get the decimal number four in, but in cannot be a decimal
number.
Right.
And is the number of sites.
So it can be either three, four, five, six, seven.
It cannot be six point five.
Right.
Therefore, the angle has to be a factor of 360 then only it will divide it.
Exactly.
What about thirty six.
Thirty 36.
360 by thirty six gives you ten.
So that's fine.
What about forty five.
Three sixty by forty five divides.
Exactly.
If you take out nine from the numerator you get forty and over here you get five.
So forty five is eight.
What about thirty.
360.
Divided by thirty.
Gives you twelve.
All of these are fine but 360 does not get perfectly divided by twenty two.
Right therefore is the answer because twenty two is not a factor of 360.
All right, let me make some space over here and please try question number three and then let's do
it together.
All right, let's do it together.
The ratio between exterior angle and interior angle of a regular polygon is giving us one by five.
We need to find the number of sites and it's mentioned it's a regular polygon.
Let's take the exterior X.
And in that case, the interior angle will be equal to five X, right.
Because it's given that the ratio is one is to five.
Now we know that the exterior angle and interior angle form a linear pair.
So they are supplementary.
That is X plus five X is equal to 180 degrees.
That gives me six.
Six is equal to 180 degree or X is 180 by six, which gives you X is equal to 30 degrees.
Therefore, the X triangle is equal to 30 degrees.
And we know that the exterior angle of a regular polygon is 360 divided by in that is equal to thirty.
So end is equal to 360 by 30, which gives you the answer as 12.