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Students, let's do this problem and equilateral triangle ABC is drawn inside a square peek, you see

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be one of the sides of the equilateral triangle coincides with the side of the square.

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Find Angle EPIK, you and BQ.

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All right.

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What's the video?

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

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All right, we're back.

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I hope you've given it a try.

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Let's do it together over here.

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It's mentioned that the equilateral triangle is ABC and the square is PKU c.B.

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So we can see that over here you have Seabourne over here.

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So you have KBE.

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And it's also mentioned that one of these sides of the equilateral triangle coincides with the site

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of the square.

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All right.

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Let's draw a rough diagram off for this question, but we have a square over here.

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Let's draw an equilateral triangle with one side equal to the side of the square.

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All right.

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So we have our figure over here.

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Let's name it.

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OK, so this is Square PKU c.B and this is Equilateral Triangle ABC.

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All right, now let's join P and AQ.

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OK, so what is asked?

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We need to find angle epicure, that's angle epicure.

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So this is one of the angles that we need to find and we need to find an gloopy HQ.

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That is this angle over here.

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All right.

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Now we know that triangle ABC is an equilateral triangle right there for each of these angles will be

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equal to 60 degrees.

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Right.

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All right.

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Now, also, we know AC is equal to Ebbie, is equal to B.S. because Triangle ABC is an equilateral

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triangle.

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All right.

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Now, over here, B.S. is equal to this side of the square.

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Right.

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So if the side of the square is equal to it, then maybe an AC is also equal to it.

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Right.

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And you can see that CQ also will be equal to it.

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Therefore, I can say that AC will be equal to you will see these two sides are also equal.

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And from an isosceles triangle, we know if two sides are equal, the angles opposite these two equal

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sides also will be equal.

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So these two angles are equal.

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Let me name them as X degree each.

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And therefore we have two equal angles over here and we know this is 60 degrees.

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And because peak UCB is a square, we know this angle over here has to be a 90 degree angle right there

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for this angle over here will be 90 minus 60, which is equal to 30 degrees.

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All right.

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Now, over here we have triangle excuse, see, and the three angles of this triangle is 30 degrees

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X.

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And therefore, from the angle some property of a triangle we can find X is equal to 180, minus 30

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by two, which gives us seventy five degrees.

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Right.

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Why is that so that because two X plus 30 is equal to 180.

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So from that we can solve X as 180 minus 30 by two, which gives us seventy five degrees.

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All right.

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Now over here you can see in a similar manner this angle also is equal to X, right.

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For this angle also is equal to the same manner as we sold over here.

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So over here we have a 60 degree angle because it's part of Triangle ABC, which is an equilateral triangle.

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All right.

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So let's move on.

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I can see that angle B A Q is equal to 360, minus 60, minus two in two X, right, because these are

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the four angles around point A and we know that one complete revolution around the point is equal to

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360 degree.

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Therefore, the sum of these four angles over here is equal to 360 degree and hence angle pacu is equal

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to 360 minus 60.

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That's this angle minus two in the seventy five because X is seventy five.

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So I'm substituting the value.

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All right, but when you solve this you will get that angle.

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B AQ is equal to 150 degrees.

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So that's one of the questions over here.

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So angle is equal to 150 degrees.

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Now let's move on.

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This angle over here also will be equal to X degree.

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Why is that so, because Bibi is A and a B is also the same side, right, because VXI, therefore Abian

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and A and B, B and C both will be equal because PKU is a square.

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Right.

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So Beeby and B are equal.

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Therefore, this angle over here and this angle over here have to be equal because they are angles opposite

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equal sides in a triangle.

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All right.

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Now over here we know that Angle B or Angle Cube is equal to 90 degrees.

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Right?

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Therefore, we can find that angle.

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AP Cube is equal to 90.

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That's this angle over here, minus X, that is 90 minus seventy five, which gives you 15 degrees.

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And that's the spot over here.

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Angle AP Q is equal to 15 degrees and that is the solution to this question.