Circle O (not shown) is divided into three sectors. Points P, Q, and R are on the circumference of the circle. Sector POR has an area of 8π, and sector ROQ has an area of 6π. If the radius of circle O is 4, what is the measure of the central angle of sector QOP, in degrees?
A. 45
B. 90
C. 135
D. 180
Answer:A
Circle O (not shown) is divided into three sectors. Points P, Q, and R are on the circumference of the circle. Sector POR has an area of 8π, and sector ROQ has an area of 6π. If the radius of circle O is 4, what is the measure of the central angle of sector QOP, in degrees?
A. 45 B. 90 C. 135 D. 180
Explanation: A Since the radius of the circle is 4, the area of the entire circle is πr2 = π(42) = 16π. Sector POR has an area of 8π and sector ROQ has an area of 6π, so the remaining sector (QOP) has an area of 16π - 8π - 6π = 2π. You can set up a proportion to determine the associated angle using the following formula: . Using the numbers you now have, your calculation will look like this: or = . Multiply both sides of the equation by 360 to determine that the sector angle is 45°, which is (A).