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In this video, let's think about the gruesome property of a quadrilateral and then we will extend it

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to the angles and property of a polygon.

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All right, let's take an example.

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We have quadrilateral ABCDE over here.

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Now I need to find the sum of Angley plus angle B plus angle C plus angle D.

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That's what we are trying to find out.

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All right.

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Let me join point E and buoyancy over here.

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OK, so you can see that I'm getting two triangles over here right now, let me mark the angles of this

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triangle, this angle one, this angle, two, three, four, five and six.

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Now we are trying to find out angle E-Plus, angle B plus angle C plus angle D.

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You can see visually that this is the same as angle one plus two plus three plus four plus five plus

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six.

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Right.

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Two is equal to B itself and five is equal to the itself.

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And you can see one plus four gives you a right.

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So you have one and four and similarly three plus six gives you see.

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So angle eight plus plus C plus these the same angle one plus two plus three plus four plus five plus.

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All right.

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Now we have learned before that the sum of the angles of a triangle is equal to 180 degrees.

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Therefore one plus two plus three is equal to 180 degrees.

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Right.

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Similarly, you can see that four plus five plus six is also equal to 180 degree.

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Therefore, angle A plus angle B plus angle C plus angle is equal to 360 degrees.

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All right.

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So the angle some of a what level is equal to 360 degrees.

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Now let's keep this aside and generalize it for a polygon over here.

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Let's analyze the relation between the number of sides and the angles.

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We have seen that in the case where the number of sites is for the angle, sum is equal to two in the

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180 or 360 degrees right now.

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Why is it doing the 180?

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Because when you have four sides, you are able to form two triangles.

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That's why you have two into the sum of the angles of a triangle that is doing the 180, which gives

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you 360.

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All right.

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Now, what would be the case if you have a five sided polygon?

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In that case, the sum of the angles will be five minus two in the 180, which is three in the 180.

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Let's see why that is.

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So over here.

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I have a Pentagon.

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That's three sides, this is four sides, and I have five sites, so this is the Pentagon now that's

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a five sided polygon, you can see that I can form.

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Three triangles, one, two, three, three triangles, therefore the angles will be three and do 180,

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and these three you get by doing five minus two.

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So let's generalize it.

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If you have an incited polygon, the angles will be equal to N minus two in two, 180 to four.

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The case where the sides were four, we got four minus two.

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That is true.

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In the case of the Pentagon, it is five minus two.

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That's three to 180.

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All right.

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Now let's try to find out what would be the measure of each internal angle.

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Now, in the case where the polygon under consideration is a regular polygon, we can find that each

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internal angle will be equal.

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Therefore, as you have in internal angles, when you have inside, each internal angle will be in minus

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two in the 180, divided by in.

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Right.

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This is the sum and each angle is equal.

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So if the measure of each angle is X degrees and you have in angles and that is equal to minus two in

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two 180, which is the sum.

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Right.

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Therefore X is equal to minus two by 180, divided by in each angle in a regular polygon will be of

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the measure and minus two in two 180 divided by an.