Step 1: Click here, then print out the page that pops up
Step 2: Cut out each shape from the print-out along the solid lines
Step 3: Fold along the dotted lines
Step 4: Put the tetrahedron inside of the cube

Notice that the bottom edge of the tetrahedron goes from corner to corner, across the bottom face of the cube.

Also notice that the center of the cube is also the center of the tetrahedron.
So, the angles in a tetrahedron are the same as from the center of a cube to the opposite corners of its bottom face.

Step 5: Remove the tetrahedron from the cube
Step 6: Draw a line inside the cube where the bottom of the tetrahedron touched (from corner to corner on the bottom face of the cube)

Now imagine a triangle sitting on that line, whose point is at the center of the cube.

We need to determine the magnitude of the angle at the top of this triangle

To help us, we'll need to recall some geometry facts...
- The diagonal of a 1x1 square is equal to the square root of 2. why?
- The diagonal of a 1x1x1 cube is equal to the square root of 3. why?
- sin(theta) = opposite/hypotenuse (for right triangles only)

So we must split our triangle into two right triangles...

sin(theta) = sqrt(2)/sqrt(3)
theta = 54.74 degrees
So the angles in a tetrahedron are 2(54.74) = 109.48 degrees