School-Safe Puzzle Games

Isosceles, a geometry puzzle

Big Thanks go out to Bilbao for submitting this one!

The seven inner triangles in the picture are isosceles. The outer big triangle is also isosceles.

What is the value of each of the angles in the picture?

Answers to this challenge can be entered into the section below; submissions will automatically be revealed when time is up!

Earlier puzzles from Bilbao:

The 12 dots

The Unreadable Account

3 Men by the Seaside


10 Comments to “Isosceles, a geometry puzzle”


  1. Shawn | PUZZLE GRANDMASTER | Profile

    My first attempt, working from right to left, yielded a big fat zero for the angle at the tip of the large isosceles triangle. Either my math is wrong, or this is a trick.


  2. suineg | PUZZLE MASTER | Profile

    Cool puzzle;
    You got 10 vars and 3 equations, so its solvable by algebra using geometry knowledge:
    Here are the equations:
    1)2a+y= 180
    2)2b +x = 180
    3)2c +z = 180
    4)2d +v = 180
    5)2e +w = 180
    6)y+b=180
    7)a+x+c=180
    8)b+z+d= 180
    9)c+v+e=180
    10)d+w= e


    The solution is 180/11= 16,36363636363636363636….. degrees, cool!


  3. bizarette18 | PUZZLE MASTER | Profile

    Big triangle:12/84/84
    Small triangles: 156/12/12; 132/24/24; 108/36/36 etc


  4. Bobo The Bear | PUZZLE MASTER | Profile

    From left to right, the isosceles triangles are:


    12-12-156
    24-24-132
    36-36-108
    48-48-84
    60-60-60
    72-72-36
    84-84-12


    Thanks, Bilbao, for letting me know that I still remember my high school geometry.


  5. Shawn | PUZZLE GRANDMASTER | Profile

    Should work for starting angle of 12 degrees.


    From left to right, the angles of the 7 triangles are:
    12,12,156
    24,24,132
    36,36,108
    48,48,84
    60,60,60 (still isosceles!)
    72,72,36
    84,84,12


    This will work for any starting triangle whose side:base ratio is 4.78339


  6. suineg | PUZZLE MASTER | Profile

    My answer was for the smallest angle or “a” because you can derivate the others form the equations and I am too lazy but here its the relantionship, b=2a; c=3a; d= 4a; e= 5a, and you can see how you get the suplementary angles x,y,v,w similarly, cool.


  7. suineg | PUZZLE MASTER | Profile

    Ok, I did not counted all the triangles cool!!!!!, I missed two triangles, big difference


  8. RK | Founder | Profile

    Very good, Shawn, Bobo The Bear, and Bizarette18 have the answers up.
    Here’s a diagram Bilbao sent along to help illustrate,


    http://www.smart-kit.com/wp-co.....lution.jpg


  9. Mihir | Profile

    From right to left the angles would be 10, 20, 30, 40, 50, 60, 70…. nice puzzle… some more please…


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