Question

In the diagram shown, AB is a diameter of circle Q.If IZABC = 40°, what is mZBAC? Explain youranswer or show your work.

Answer 1

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.

`\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}`

Hence, the angle BAC measures 50°.