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In this video, let's learn an interesting property about sightly Quadratus.

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Now, first, let's try to understand what do we mean with this cyclic quadrilateral?

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All right, over here I have a circle and I have a quadrilateral over here.

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Now, you can see that all the vertices that is all these four pieces of the quadrilateral are on the

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circle.

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This type of a quadrilateral is called Acyclic Quadrilateral.

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So over here, ABCDE is a cyclic quadrilateral already.

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Now, in cycling quadrilaterals, the opposite angles are supplementary.

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That is angle a plus angle.

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See over here is equal to 180 degrees and in a similar manner.

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Angle B plus angle D also is equal to 180 degrees.

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Now this is an important property.

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Let's quickly try to understand why the opposite angles in a cyclic quadrilateral are supplementary

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SailPoint or is the center of the circle.

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And this is that center.

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Let me join B with Orb and let me join David or.

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All right, now, let's take that this angle over here is to Alpha and let this over here be to Beta.

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All right, now we know that angle B, C, D is the angle subtrend that by the arc beardie, right?

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The minor arc beardie.

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Therefore we can see that angle B, C, D, let me right that over here.

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Angle BCT will be equal to half the measure of Arc B, right.

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Which is equal to two alpha.

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So ABCDE will be equal to two alpha divided by two which is equal to Alpha.

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Similarly you can see that angle B 80, that's angle B 80 will be equal to off to beta.

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Right.

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So that's two beta divided by two which gives you beta.

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Now over here you can see that two alpha plus two beta is making one complete revolution around the

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center.

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So two alpha plus two beta is equal to 360 degree.

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Right.

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Therefore, we can see that Alpha plus beta is 360 by two.

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That's equal to 180 degrees.

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That's why we say that in the case of a cyclic quadrilateral, the opposite angles are supplementary.