Mathematics

The key is recognizing that a sector is just a "slice" of the circle, and its area is proportional to the angle it subtends. Use the sector area formula $A = \frac{\theta}{360°} \times \pi r^2$ (or with radians) to find what fraction of the full circle this sector represents, then solve for the central angle $\theta$. Once you have the angle, you can find any other property of that sector, like its arc length or perimeter.

The key is recognizing that a sector is just a "slice" of the circle, and its area is proportional to the angle it subtends. Use the sector area formula $A = \frac{\theta}{360°} \times \pi r^2$ (or with radians) to find what fraction of the full circle this sector represents, then solve for the central angle $\theta$. Once you have the angle, you can find any other property of that sector, like its arc length or perimeter.