What is the sum of the measures of angles A, B, C, D, and E?
I really need at least some kind of hint here, because I have no idea where to begin. No information is given for the picture.
I have added five letters to your diagram.
The sum of the angles in the pentagon, KJLMN, is . WHY?
In the sum .
Moreover, by the external angle theorem .
If you do this for each of the other four “external triangles” and all five you will see the answer.
Since the given figure can be transformed by a sequence of such moves into a regular pentagram, the angle sum of the regular pentagram is equal to the angle sum of the given figure.