3. Given a Pentagram

If the pentagon is regular, that means that all the angles are the same. Since the angles in a pentagon add up to 3x180 = 540o, it follows that they are all 540/5 = 108o. Since the pentagon is regular, that means that triangles ABC, BCD, CDE, DEA, and EAB are all isosceles triangles. Since the vertex angles are all 108o, the other angles are all 36o.

At this point we can see that triangles ABF, BCG, CDH, DEI, and EAJ are all isosceles triangles, so we can fill in the remaining angles in those triangles.

We can now fill in the supplementary and vertical angles at points F, G, H, I, and J

Finally, there are two ways to look at the vertex angles in triangles AFJ, BFG, CGH, DHI, and EIJ. It is either the last angle in those triangles, or what remains to be filled in of the outer 108o angles.

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