Final answer:
To find the measure of angle BAC, we need to find the measure of the entire central angle of the circle. We can set up the equation using the area ratio of the shaded sector to the entire circle. By substituting the given values and simplifying, we find that m angle BAC is equal to 144°.
Step-by-step explanation:
To find the measure of angle BAC, we first need to find the measure of the entire central angle of the circle. The area ratio of the shaded sector to the entire circle is equal to the ratio of the measure of the central angle of the shaded sector to the measure of the entire central angle of the circle. Therefore, we can set up the equation:
Area of shaded sector / Area of entire circle = m angle BAC / 360°
Substituting the given values, we have:
10π / π(AB)² = m angle BAC / 360
Simplifying the equation, we get:
m angle BAC = 360 * (10π / π(AB)²)
Substituting AB = 5, we can simplify further:
m angle BAC = 360 * (10π / π(5)²)
m angle BAC = 360 * (10π / 25π)
m angle BAC = 360 * (10/25)
m angle BAC = 144°