In a triangle ABC, ∠ABC = 75° and ∠ACB = $$\frac{{{\pi ^c}}}{4},$$  the circular measure of ∠BAC is?

A. $$\frac{{5\pi }}{{12}}$$ radian

B. $$\frac{\pi }{3}$$ radian

C. $$\frac{\pi }{6}$$ radian

D. $$\frac{\pi }{2}$$ radian

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & \frac{{{\pi ^c}}}{4}{\text{ = }}\frac{{{{180}^ \circ }}}{4}{\text{ = }}{45^ \circ } \cr & \angle {\text{BAC}} = {180^ \circ } - {75^ \circ } - {45^ \circ } = {60^ \circ } \cr & {180^ \circ } \to \pi \cr & {1^ \circ } \to \frac{\pi }{{{{180}^ \circ }}} \cr & {60^ \circ } \to \frac{\pi }{{{{180}^ \circ }}} \times {60^ \circ } = \frac{\pi }{3}{\text{ radian}} \cr} $$