For a circle with a radius of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 5 2 π meters? a: 50 b: 75 c: 90 d: 120

The answer is 75 degrees    arc length = (radian central angle)  · (radius)i'll assume you meant (5/2)π as the length.rearrange above for angle to get    radian angle  = (arc length) / (radius)    radian angle= (5π/2) / 6since division is just multiplying by reciprocal    radian angle = (5π/2)  · (1/6)    radian angle  = (5π/12)convert from radians to degrees: π radians = 180 degrees    degree angle = (radian angle)  · ( 180°/(π radians) )    degree angle = (5π/12)  · 180°/π    degree angle = (5π/12)  · 180°/π    degree angle = (5/1)  · 15°    degree angle = 75°