To determine the angle subtended by a sector at the center of a circle, you can use the following formula:

This formula relates the arc length of the sector to the radius of the circle. It is derived from the fact that the circumference of a circle is given by $2\pi r$, where $r$ represents the radius.

To begin, you need to know the arc length of the sector, which is the distance measured along the curved edge of the sector. Let’s denote the arc length as $L$ and the radius as $r$. The angle subtended at the center of the circle (in radians) can be calculated as:

However, since angles are frequently expressed in degrees in GCSE Maths, we must convert the angle from radians to degrees. Given that there are $180$ degrees in $\pi$ radians, we multiply the angle in radians by $\frac{180}{\pi}$ to obtain the angle in degrees:

For example, let’s consider a scenario where the arc length is $10$ cm and the radius is $5$ cm. The angle in radians can be calculated as follows:

To convert this angle to degrees, we perform the following calculation:

Therefore, the angle subtended by the sector at the center of the circle is approximately $114.59$ degrees.