They are given 31 angle measures: 10, 11, 25, 25, 40, 40, 53, 57, 72, 72, 73, 74,

Then they are asked to use each angle measure exactly once to create the following polygons:

4 distinct triangles

2 distinct quadrilaterals

1 pentagon

1 hexagon

Then they're asked to sketch each one and write a short paragraph telling how they know their answers are correct.

So, I'm interested to know if people can successfully come up with a solution without knowing the answer first, and if there are multiple possible answers. I'm also curious to know how long it takes people to do something like this.

I covered up the answer and gave it a try. My first attempt started with trying to find the 4 triangles. I found 3, but then it was impossible to find a 4th. Was I just unlucky? Did avoiding the first obvious triangle (because I had already seen the answer) screw me up?

All of the other activities were relatively reasonable (if stupid). It's just this last one that looks to be a bear.