If I understand the use of "reciprocal" correctly, the answer is 249 degrees.
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11 over 8
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YES!!! it is 360 - 117 = 243 For bearing (navigation) . Bearing of due North is bearing zero(0) . Then moving around the compass clockwise due East is bearing 090 , die South is bearing 180 and due West is bearing 270 . However, if starting at bearing zero(0) and moving ANTI-Clockwise , the first bearing is 270 , which is 90 degrees of turn. The 90 degrees in anti =clockwise is the inverse. NB For ALL bearings you quote three digits. So due East , bearing 90 is quoted as '090'. This is normal navigational practice.
It is 0. But some people say 0 does not have a reciprocal.
Reciprocal of 3 is 1/3 Reciprocal of 35 is 1/35. Reciprocal of x is 1/x. Reciprocal of 1/3 is 3. Reciprocal of 1/x is x. It is the inverse of a number.