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Let's do this question who is the center of Triangle Park, you are all right.

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Find angle Q or if angle Q is angle or is equal to sixty five degrees.

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All right.

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Pause the video, give it a try and then let's do it together.

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All right.

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We're back.

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I hope you've given it a try.

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Let's do it together.

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It's given that these two angles are sixty five degrees.

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Right.

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Therefore as for the angle some property of a triangle we can see that angle is equal to 180 minus sixty

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five plus sixty five.

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That's one thirty over here.

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And you get angle B is equal to fifty degrees.

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All right.

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Now over here, always the center and this circle is the inner circle of Triangle Park.

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You are therefore these lines you, you are and B are tangents to this circle at these points.

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Let's join these points to.

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All right.

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Now, because P, Q, R and B are tangents to this circle.

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Therefore these angles are ninety degrees.

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Remember a tangent to a circle.

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Meets the circle only at one point, and if you join that point, for example, in this case, this

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point to the center right, the angle formed with the center, the point of intersection and the tangent,

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this angle over here will be 90 degrees.

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All right.

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Now, let me mark these three points as a point A, point B and point C.

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Now let's check quadrilateral A, B, B, or you can see that learning A, B, B is a kite.

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What is a kite?

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A kite is a special type of quadrilateral where two sets of Adderson sides are equal or hear it or and

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or B are radiuses of the inner circle.

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So these two sides are equal and Eppy and B, we are also equal because these are the engines from an

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external point to a circle.

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Right now, these two things to learn more about it, check the section where we discuss Sakalys in

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great depth.

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Now, inner circle, if you draw Tandan students are from an external point, like in this case from

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point B, which is an external point to this circle.

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We are drawing tangents P, Q and B are right.

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In that case, we will be equal to be B.

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This is a property that we learn in circles now because of that, because these two sides are equal

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and these two sides are equal.

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Therefore, APB is a kite.

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All right.

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Let's just note that over here now you can see that this angle is ninety degrees.

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This angle is ninety degree.

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Right.

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And this angle over here, that's angle P is 50 degrees.

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Now, we have seen that the sum of the angles of a triangle is 180 degrees.

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Right.

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So what will be the sum of the angles of a quadrilateral?

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If you have any quadrilateral, you can see that you can split it and make it into two triangles for

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this angle plus this angle.

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Plus this angle gives you a 180 degree.

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Similarly, this angle plus this angle, plus this angle gives you 180 degrees.

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Therefore, the sum of the internal angles of a quadrilateral is 180 plus 180.

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That's 360 degree.

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Now you will learn more about this under the section of quadrilaterals.

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All right.

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I'm just listing it out here because I wanted this to be linked with incentive, which is a topic that

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we have learned in this section.

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All right, now, because angle B plus angle over here and angle B over here and angle it or B is equal

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to 360 degree.

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Therefore, I can say that angle all is equal to 360, minus 90, minus 90, minus 50.

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Right.

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Let me quickly write that over here.

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What is it that we've just discussed?

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360 is equal to angle.

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It will be.

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Plus Angle or AP.

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Plus Angle or Beebee.

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Plus angle, Pete, right?

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So these are the four internal angles of this quadrilateral.

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Now we know that angle is.

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B is what we are trying to find, but that's what we have put us angle or here angle or a B is 90 degrees

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angle or B, B is 90 degrees and angle is equal to 50 degrees.

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So that's why Angle is equal to 360, minus 90, minus 90, minus 50.

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All right.

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Let me make some space over here.

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Now or here, we get that angle or is equal to 130 degrees, all right, now you can see that quadrilaterals

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E or C, Q and B or C, R, that's E or CQ, this one over here, and B or C, R, this one over here.

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These are also kite's.

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Why is that so?

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It's the same reason over here, for example, in AC.

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Q Q is equal to QC because these are tangents to a circle from an external point.

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Q And is equal to or C because these are in radiuses and the radius is the same.

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All right.

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Now these are kite's.

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Now, let me join you and or OK, now indicate the longer diagonal is an angle by sector.

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So that's why I can say that this angle and this angle are equal.

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Similarly, this angle on this angular equal now learn more about heights in this section under quadrilaterals.

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I'm just listing out here because I don't want it to be completely separated.

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In your mind, this is related to topics in quadrilaterals and circles and triangles, right?

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We have an instructor over here.

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That's something that we've learned in triangles.

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We have a concept of Kate over here.

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That's something that we learn in quadrilaterals and we have tandem's over here, which we learn under

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circles.

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So it's a multi concept question.

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All right.

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Now let's press on.

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So AOK, you and are kites and indicate the longer diagonal is an angle by sector.

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Let me just quickly explain that over here.

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So I have a Kate over here.

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This is the shape of a guide.

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These two sides are equal.

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These two sides are equal.

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Now to diagonals can be formed.

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This is the longer diagonal, right?

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This is the longer diagonal.

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This is the shorter diagonal.

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Now, the longer diagonal is an angle bisecting.

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So this angle will be equal to this angle and this angle will be equal to this angle.

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That's the property that we have used over here.

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QOL is the longer diagonal of AoE CQ.

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That's why Angle A OCU and Angle C or Q are equal and I've marketed as X and X.

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Similarly, Anglesey or R and Angle R or B are equal because or is the bigger diagonal of quadrilateral

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B or C R.

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That's why I've marked as white and white.

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Now you can see that X plus X plus Y plus white.

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That is two X plus two Y is equal to 360 minus this angle over here, which is angle it will be or we

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have marked angle B over here and this angle is one thirty degree.

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Right.

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Therefore X plus X plus Y plus Y that's two plus two.

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Y is equal to 360 minus one thirty which is equal to thirty now therefore we can find that angle Q or

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R which is angle X plus angle Y over here.

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That would be half of to thirty.

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Right.

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Or X plus why is equal to two thirty by two.

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That gives you your answer as one hundred and fifteen degrees.