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Let's do this questions the Polyana in which some of all exterior angles is equal to the sum of the

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interior angles is covered.

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All right, pose the video, give it a try, and then let's do it together.

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All right, let's do it together.

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I hope you have given it a try.

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Now, the sum of all exterior angles in a polygon we have seen is equal to 360 degree.

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Right.

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And what is the sum of interior angles if there are inside?

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The sum of interior angles will be equal to and minus two in two 180.

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Now, in this question, it's mentioned that these two are equal.

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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

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to four.

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Is it quadrilateral.

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Right to the sum of the exterior angles in a column is equal to 360 degree.

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And we have seen that the sum of the interior angles inequality is equal to 360 degrees.

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So the answer over here is quadrilateral.

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All right, let's go to the next question.

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Which of the following can never be the measure of the exterior angle of a regular polygon?

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Was the video.

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Give it a try and then let's do it together.

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All right.

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Let's do it together.

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We know that in the case of a regular polygon, the exterior angle is equal to three sixty, divided

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by N, right.

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So therefore N is equal to 360, divided by the exterior angle now.

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So it has to divide.

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Exactly right.

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Therefore, the answer to this question.

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Is equal to option eight, that's 22, right?

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Why is that so?

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Why should it divide exactly?

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If it does not divide exactly, you will get the decimal number four in, but in cannot be a decimal

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number.

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Right.

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And is the number of sites.

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So it can be either three, four, five, six, seven.

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It cannot be six point five.

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Right.

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Therefore, the angle has to be a factor of 360 then only it will divide it.

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Exactly.

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What about thirty six.

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Thirty 36.

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360 by thirty six gives you ten.

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So that's fine.

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What about forty five.

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Three sixty by forty five divides.

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Exactly.

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If you take out nine from the numerator you get forty and over here you get five.

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So forty five is eight.

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What about thirty.

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360.

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Divided by thirty.

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Gives you twelve.

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All of these are fine but 360 does not get perfectly divided by twenty two.

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Right therefore is the answer because twenty two is not a factor of 360.

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All right, let me make some space over here and please try question number three and then let's do

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it together.

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All right, let's do it together.

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The ratio between exterior angle and interior angle of a regular polygon is giving us one by five.

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We need to find the number of sites and it's mentioned it's a regular polygon.

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Let's take the exterior X.

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And in that case, the interior angle will be equal to five X, right.

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Because it's given that the ratio is one is to five.

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Now we know that the exterior angle and interior angle form a linear pair.

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So they are supplementary.

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That is X plus five X is equal to 180 degrees.

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That gives me six.

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Six is equal to 180 degree or X is 180 by six, which gives you X is equal to 30 degrees.

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Therefore, the X triangle is equal to 30 degrees.

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And we know that the exterior angle of a regular polygon is 360 divided by in that is equal to thirty.

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So end is equal to 360 by 30, which gives you the answer as 12.