Jack: you're on fire.I believe that you don't need the given '108' angle. Because the pentagon is regular and the line is going through two fixed points it doesn't seem absolutely necessary.On the other hand, I tried to solve it without the 108 and it seemed substantially harder.I like this problem. I think it can be linked to the star angle problem from the investigation sheet if you expand to any odd # sided regular polygon.
Solving it without the 108 can't be that much harder. We know the interior angle of a pentagon is 108, and because the line cuts the pentagon into a triangle (the quadrilateral is not important), the easiest way to solve this is by solving the other two angle as you would do for a triangle instead of starting at the given 108.