## 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:

Shawn| PUZZLE GRANDMASTER | Profile September 8th, 2011 - 10:11 amMy 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.

suineg| PUZZLE MASTER | Profile September 8th, 2011 - 5:42 pmCool 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!

bizarette18| PUZZLE MASTER | Profile September 8th, 2011 - 5:48 pmBig triangle:12/84/84

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

Bobo The Bear| PUZZLE MASTER | Profile September 8th, 2011 - 11:49 pmFrom 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.

Shawn| PUZZLE GRANDMASTER | Profile September 9th, 2011 - 9:07 amShould 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

suineg| PUZZLE MASTER | Profile September 9th, 2011 - 8:47 pmMy 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.

suineg| PUZZLE MASTER | Profile September 14th, 2011 - 6:00 pmOk, I did not counted all the triangles cool!!!!!, I missed two triangles, big difference

RK| Founder | Profile September 14th, 2011 - 8:20 pmVery good, Shawn, Bobo The Bear, and Bizarette18 have the answers up.

Here’s a diagram Bilbao sent along to help illustrate,

http://smart-kit.com/wp-conten.....lution.jpg

cece| Profile February 20th, 2012 - 6:31 amcool !

Mihir| Profile May 23rd, 2012 - 7:31 amFrom right to left the angles would be 10, 20, 30, 40, 50, 60, 70…. nice puzzle… some more please…

wizzle2006| Profile February 9th, 2015 - 3:03 pmDoes anyone want to explain how to solve this please!???!(: