jmc

The measure of each interior angle in a regular $n$-gon is $180(n-2)/n$ degrees. Therefore, the measure of angle $\angle BAD$ is $180(7-2)/7=\frac{900}{7}$ degrees and the measure of angle $CAD$ is 90 degrees. The angle, $\angle BAC$, therefore can be expressed as: $$360^{\circ }-{\frac{900}{7}}^{\circ }-90^{\circ }=270^{\circ }-{\frac{900}{7}}^{\circ }={\frac{1890-900}{7}}^{\circ }=\boxed{{\frac{990}{7}}^{\circ }}.$$