In a triangle $\mathrm{ABC}, \angle \mathrm{ABC}=75^{\circ}$ and $\angle \mathrm{ACB}=\frac{\pi^{\mathrm{c}}}{4}$. The circular measure of $\angle \mathrm{BAC}$ is

∠ABC = 75°

180° = π radian

$\therefore 75^{\circ}=\frac{\pi}{180} \times 75=\frac{5 \pi}{12}$ radian

$\therefore \angle \mathrm{BAC}=\pi-\frac{\pi}{4}-\frac{5 \pi}{12}$

$=\frac{12 \pi-3 \pi-5 \pi}{12}=\frac{4 \pi}{12}$

$=\frac{\pi}{3}$ radian