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An arc of 5/6 the circumference of a circle subtends a central angle of how many degrees?

A) 60 degrees
B) 120 degrees
C) 150 degrees
D) 180 degrees

1 Answer

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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.

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