Final answer:
An arc that is 5/6 of the circumference of a circle subtends a central angle of 300 degrees, which is found by multiplying 360 degrees by 5/6.
Step-by-step explanation:
The question asks to find the central angle of a circle subtended by an arc that is 5/6 of the circumference of the circle. The circumference of a circle is related to its diameter or radius and can be calculated as 2πr. We know that a circle represents 360 degrees, so if the arc is 5/6 of the full circumference, the central angle will proportionally be 5/6 of 360 degrees.
To find the central angle, we multiply 360 degrees by 5/6:
(5/6) × 360 = 300 degrees
Therefore, an arc of 5/6 the circumference of a circle subtends a central angle of 300 degrees.