Can you find the Angle X in these Squares? | Fast & Easy Explanation

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[anatoliy]

What a beautiful task! Your lessons are a real pleasure, Sir. Thank you very much for meeting you on the Internet. I hope to meet you live someday!

[sandanadurair]

in top 9-sided polygon total internal angle = (9-2)*180 = 1260
sum of the given angles = 90+90+62+270+x+270+43+270+59 ==>x+1154
x+1154 =1260
x = 1260-1154 = 106

[davidfromstow]

I hadn't a clue where to start, but as soon as I saw your parallel lines, I knew how to proceed. Thank you for another great question/lesson!

[Copernicusfreud]

I solved the problem using a much longer method. I drew perpendiculars from the tops of the squares to the top of the rectangle creating quadrangles and pentangles and then drawing circles around the top angles of the squares where they formed intersections for my quadrangles and pentangles. The sum of the angles in the quadrangles = 360. The sum of the angles in the pentangles = 540. The sum of the angles inside the circles at the top of the squares = 360. I was able to figure the angles of the pentangles and quadrangles by simple subtraction. Eventually, I came to angle x, and the angle was 106 degrees. The angles for the final pentangle with x were 152, 90, 90, 102, and angle x = 106.

[math]

interesting question, great solution, thanks for sharing

[Chrisoikmath_]

This problem is my favorite! ❤❤
You are the best teacher! 👌
Keep it up!😀😀

[srividhyamoorthy]

Nice always waiting for next video thanks

[rahulpaul]

Very great way to solved this problem sir 👍

[opytmx]

x = 28" (opposite at the right square) + 78° (opposite to 90-12 at the middle square) = 106°

[montynorth]

So visually, if the yellow square was not tilted, then X would be 90 + 28.
Since the yellow square is tilted clockwise by 12 (43 -31) then X = 90 + 28 -12

[matijaderetic]

I just added rotations so they end up in an integer multiple of 90°.
So clockwise rotations of 59+43+x+62=k•90
164+x=k•90
x=16+k•90
x=106

[rifatshan]

Sir, , after you drew the parralal lines, i don't know how but my brain suddenly became sharp and i got the answer 🙂, first step was totally unknown to me😅. Thanks for teaching this new way, this can help me in future.
🙂🙂

[luis]

I imagine the square (the size of the square can be always the same) as a vehicle going from one position to the next, by changing its direction. 31-43+(180-x)=90-28

[philipkudrna]

Before watching and „in my head“: 31-43+90+28=106 degrees.

[mustafizrahman]

I have failed to solve it many days later.

[Waldlaeufer]

1) The green square is rotated 31° to the left.
2) The yellow square is rotated 43° to the right in relation to the green square. It is therefore rotated 43°-31°=12° to the right. Compared to the red square, however, you can also say that it is rotated 90°-12°=78° to the left.
3) The red square is rotated 28° to the right. The angle between the yellow and the red square is therefore 78°+28°=106°.