The angle (in degrees) made by a sector having area one-sixth of the area of a semicircle is

To find the angle of the sector, we use the area formulas for a circle and its parts. The area of a circle is πr², and the area of a semicircle is half of that, or (1/2)πr². The area of a sector with a central angle θ is given by (θ/360°) × πr². According to the problem, the sector's area is one-sixth of the semicircle's area. Mathematically, this is expressed as (θ/360°) × πr² = (1/6) × (1/2)πr². By canceling πr² from both sides, the equation simplifies to θ/360° = 1/12. Solving for θ, we multiply 360° by 1/12, which equals 30°. Therefore, the central angle of the sector is 30°, which corresponds to option 2.