It's important to know that an angle inscribed in a semi-circle is a right angle. So, the angle ACB is equal to 90°.
Given that the angle ABC is 40°, we can use the sum of interior angles theorem to find the missing angle.
[tex]\begin{gathered} m\angle ABC+m\angle ACB+m\angle BAC=180 \\ 40+90+m\angle BAC=180 \\ m\angle BAC=180-130 \\ m\angle BAC=50 \end{gathered}[/tex]