$52.$An ammonia compressor is driven by a $20-$kW motor. The compressor and the motor rpm are $360$ and $1750,$ respectively. The small sheave has a pitch diameter of $152\mathrm{.}4$ mm$.$ If the belt to be used is standard C$-120,$ determine the arc of contact? Note: L $=122\mathrm{.}9$ inches.

A$.148\mathrm{.}2$ degrees

B$.158\mathrm{.}2$ degrees

C$.128\mathrm{.}2$ degrees

D$.138\mathrm{.}2$ degrees

Note: The correct answer is be $\text{'}138\mathrm{.}2\text{'}$ degrees, please justify.