Question

b 150° a ? c

Explanation:

Step1: Find the measure of the arc opposite to the inscribed angle

The measure of an inscribed angle is half the measure of its intercepted arc. The total measure of a circle is \(360^{\circ}\). Given one arc is \(150^{\circ}\), the arc opposite to the inscribed angle \(\angle BAC\) is \(360^{\circ}- 150^{\circ}=210^{\circ}\). But wait, no! Wait, actually, the inscribed angle \(\angle BAC\) intercepts an arc. Wait, no, the formula is: The measure of an inscribed angle \(\theta\) is \(\theta=\frac{1}{2}\text{(measure of intercepted arc)}\). The intercepted arc here: If we consider the inscribed angle \(\angle BAC\), the intercepted arc is \(150^{\circ}\) (assuming the standard circle - angle - arc relationship as per the figure's given \(150^{\circ}\) arc).

Step2: Calculate the inscribed angle

Using the formula for an inscribed angle \(\angle BAC=\frac{1}{2}\times\) (measure of intercepted arc). Substituting the value of the intercepted arc \(= 150^{\circ}\), we get \(\angle BAC=\frac{1}{2}\times150^{\circ}\)

Answer:

\(75^{\circ}\)