Students, let's do this problem and equilateral triangle ABC is drawn inside a square peek, you see
be one of the sides of the equilateral triangle coincides with the side of the square.
Find Angle EPIK, you and BQ.
All right.
What's the video?
Give it a try and then let's do it together.
All right, we're back.
I hope you've given it a try.
Let's do it together over here.
It's mentioned that the equilateral triangle is ABC and the square is PKU c.B.
So we can see that over here you have Seabourne over here.
So you have KBE.
And it's also mentioned that one of these sides of the equilateral triangle coincides with the site
of the square.
All right.
Let's draw a rough diagram off for this question, but we have a square over here.
Let's draw an equilateral triangle with one side equal to the side of the square.
All right.
So we have our figure over here.
Let's name it.
OK, so this is Square PKU c.B and this is Equilateral Triangle ABC.
All right, now let's join P and AQ.
OK, so what is asked?
We need to find angle epicure, that's angle epicure.
So this is one of the angles that we need to find and we need to find an gloopy HQ.
That is this angle over here.
All right.
Now we know that triangle ABC is an equilateral triangle right there for each of these angles will be
equal to 60 degrees.
Right.
All right.
Now, also, we know AC is equal to Ebbie, is equal to B.S. because Triangle ABC is an equilateral
triangle.
All right.
Now, over here, B.S. is equal to this side of the square.
Right.
So if the side of the square is equal to it, then maybe an AC is also equal to it.
Right.
And you can see that CQ also will be equal to it.
Therefore, I can say that AC will be equal to you will see these two sides are also equal.
And from an isosceles triangle, we know if two sides are equal, the angles opposite these two equal
sides also will be equal.
So these two angles are equal.
Let me name them as X degree each.
And therefore we have two equal angles over here and we know this is 60 degrees.
And because peak UCB is a square, we know this angle over here has to be a 90 degree angle right there
for this angle over here will be 90 minus 60, which is equal to 30 degrees.
All right.
Now, over here we have triangle excuse, see, and the three angles of this triangle is 30 degrees
X.
And therefore, from the angle some property of a triangle we can find X is equal to 180, minus 30
by two, which gives us seventy five degrees.
Right.
Why is that so that because two X plus 30 is equal to 180.
So from that we can solve X as 180 minus 30 by two, which gives us seventy five degrees.
All right.
Now over here you can see in a similar manner this angle also is equal to X, right.
For this angle also is equal to the same manner as we sold over here.
So over here we have a 60 degree angle because it's part of Triangle ABC, which is an equilateral triangle.
All right.
So let's move on.
I can see that angle B A Q is equal to 360, minus 60, minus two in two X, right, because these are
the four angles around point A and we know that one complete revolution around the point is equal to
360 degree.
Therefore, the sum of these four angles over here is equal to 360 degree and hence angle pacu is equal
to 360 minus 60.
That's this angle minus two in the seventy five because X is seventy five.
So I'm substituting the value.
All right, but when you solve this you will get that angle.
B AQ is equal to 150 degrees.
So that's one of the questions over here.
So angle is equal to 150 degrees.
Now let's move on.
This angle over here also will be equal to X degree.
Why is that so, because Bibi is A and a B is also the same side, right, because VXI, therefore Abian
and A and B, B and C both will be equal because PKU is a square.
Right.
So Beeby and B are equal.
Therefore, this angle over here and this angle over here have to be equal because they are angles opposite
equal sides in a triangle.
All right.
Now over here we know that Angle B or Angle Cube is equal to 90 degrees.
Right?
Therefore, we can find that angle.
AP Cube is equal to 90.
That's this angle over here, minus X, that is 90 minus seventy five, which gives you 15 degrees.
And that's the spot over here.
Angle AP Q is equal to 15 degrees and that is the solution to this question.