Diagonals of a Heptagon

Let the heptagon be $ABCDEFG$ . Draw $\overline{AC}$ and $\overline{GD}$ . Now use Ptolemy's theorem on $ACDG$ to obtain $ab+1=b^2 \rightarrow b=\dfrac{\sqrt{a^2+4} + a}{2}$ Use Law of Cosines on $\Delta ABC$ to obtain $a^2 = \sqrt{2-2\cos(\dfrac{900}{7})}$ . This can be calculated to approx. $1.80194$ . Now we plug this into our original equation to get $b \approx 2.24698$ . Thus $a-b \approx 0.44504$ and $100(a-b) \approx 44.504$ rounds to $\boxed{45}$ .