A sector of a circle is an area division of that circle. The components of the sector include its inner angle, the circle's radius that creates the adjacent sides of the inner angle, and the length of the circle's circumference between the lengths of the two radii. Measure the angle of the sector in both radians and degrees by using the sector's area, its arc length and the radius of the circle.
Multiply the area of the sector by 2. For example, the area of the circle is 120 cm^2. Therefore, 120 x 2 = 240 cm^2.
Divide that amount by the radius squared. For the example, the radius is 15, and 15 x 15 = 225. Therefore, 120 x 225 = 0.5333 radians. The measurement of the inner angle of the sector is 0.5333 radians.
Multiply the measurement in radians by 180, then divide by π, or pi, which is a mathematical constant that begins with 3.14. For the example, 0.5333 x 180 = 96. Next, 96/π = 30.5577. The angle is 30.5577 degrees.
Divide the length of the sector's arc by the radius to obtain the measurement of the inner angle. For example, if the arc length is 15 cm and the radius is 10 cm, then the measurement of the angle in radians is 15/10 = 1.5 radians.
Multiply the measurement of the inner angle in radians by 180, then divide it by π to obtain the angle's measurement in degrees. For the example, 1.5 x 180 = 270, and 270/ π = 85.9437 degrees.