When a circle is divided into sectors, the sum of the central angles of those sectors will always be 360 degrees. This can be justified using the concept that a full circle has a total of 360 degrees.
In a circle, the central angle of each sector is defined as the angle formed at the center of the circle by the two radii that bound the sector. Since the circle is divided into 8 equal sectors, each sector covers an equal portion of the circle, representing 1/8th of the total area.
Since a full circle represents 360 degrees, dividing it into 8 equal sectors means that each sector covers 1/8th of 360 degrees. Mathematically, this can be expressed as:
1/8 * 360 degrees = 45 degrees
Thus, each sector has a central angle of 45 degrees. As there are 8 sectors in total, the sum of their central angles can be calculated as:
8 * 45 degrees = 360 degrees
Therefore, the sum of the central angles of the 8 sectors in the circle is 360 degrees, which corresponds to the measure of a full circle.