The problem asks to find the angle $\angle BAC$ given that the angle $\angle ACB = 40^\circ$ in the circle.

In the image, we can see that the triangle $ABC$ is inscribed in a circle. One key property of a cyclic quadrilateral (or inscribed triangle) is that the angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at any point on the circumference.

For this problem:

• The angle $\angle ACB = 40^\circ$.
• The angle $\angle BAC$ and $\angle ACB$ subtend the same arc $BC$, meaning they are related by the inscribed angle theorem.

Using the inscribed angle theorem: $\angle BAC = \angle ACB$ Thus: $\angle BAC = 40^\circ$

So, the correct answer is 40 degrees.

Would you like more details or have any questions?

Here are some related questions to explore:

1. What is the inscribed angle theorem, and how does it apply to this problem?
2. Can you explain how angles subtended by the same arc are related?
3. What is the difference between central angles and inscribed angles?
4. How do we calculate the other angles of a triangle inscribed in a circle if more information is given?
5. What are the properties of a cyclic quadrilateral in a circle?

Tip: Always remember that the inscribed angle theorem states that the angle subtended by an arc at the center is twice the angle subtended at the circumference.