alison jogging  on a circular track that has a radius of 140 feet. she uns along the track from poin R to point N , a distance of 230 feet. find the nearest degree, the measure of minor arc N

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The principle is that radians times the radius equals the arc length.  2pi radians = 360 degrees.  You can see this principle work in the circumference formula 2pi r = C.  For your problem; The angle for arc RN in radians = 230 / 140 or 23/14 radians = 1.64286 rad Change this to degrees as follows: 2pi / 1.64286 = X / 360         Solve for X by multiplying both sides by 360 X = 94.12878 degrees.  To the nearest degree its 94 deg.