Question: Do (a) top-left: hexagon A-B-C-D-E-F with a north arrow inside; sides are labeled A\to B N41d35'E, B\to C, C\to D, D\to E, E\to F, F\to A, with interior angles 129d11', 88d35', 132d30', 135d42', 118d52', and 115d10'.

1. **Problem Statement:** We are given a hexagon A-B-C-D-E-F with side bearings and interior angles. We want to find the azimuths (bearings) of each side starting from A\to B. 2. **Given Data:** - Bearing of A\to B: $N41^\circ35'E$ which is $41^\circ35'$ azimuth. - Interior angles at vertices: $129^\circ11'$, $88^\circ35'$, $132^\circ30'$, $135^\circ42'$, $118^\circ52'$, $115^\circ10'$. 3. **Formula and Rules:** - Azimuth of next side = Azimuth of previous side + $180^\circ$ - interior angle at vertex (if turning clockwise). - Bearings are measured clockwise from north. - Convert all angles to decimal degrees for calculation, then back to degrees and minutes. 4. **Step-by-step Calculation:** - Convert $41^\circ35'$ to decimal: $41 + \frac{35}{60} = 41.5833^\circ$. - Starting azimuth $A\to B = 41.5833^\circ$. - At vertex B, interior angle = $129^\circ11' = 129 + \frac{11}{60} = 129.1833^\circ$. - Azimuth $B\to C = A\to B + 180^\circ - 129.1833^\circ = 41.5833 + 180 - 129.1833 = 92.4^\circ$. - At vertex C, interior angle = $88^\circ35' = 88.5833^\circ$. - Azimuth $C\to D = B\to C + 180^\circ - 88.5833 = 92.4 + 180 - 88.5833 = 183.8167^\circ$. - At vertex D, interior angle = $132^\circ30' = 132.5^\circ$. - Azimuth $D\to E = C\to D + 180^\circ - 132.5 = 183.8167 + 180 - 132.5 = 231.3167^\circ$. - At vertex E, interior angle = $135^\circ42' = 135.7^\circ$. - Azimuth $E\to F = D\to E + 180^\circ - 135.7 = 231.3167 + 180 - 135.7 = 275.6167^\circ$. - At vertex F, interior angle = $118^\circ52' = 118.8667^\circ$. - Azimuth $F\to A = E\to F + 180^\circ - 118.8667 = 275.6167 + 180 - 118.8667 = 336.75^\circ$. 5. **Convert azimuths back to degrees and minutes:** - $B\to C = 92.4^\circ = 92^\circ 24'$. - $C\to D = 183.8167^\circ = 183^\circ 49'$. - $D\to E = 231.3167^\circ = 231^\circ 19'$. - $E\to F = 275.6167^\circ = 275^\circ 37'$. - $F\to A = 336.75^\circ = 336^\circ 45'$. 6. **Summary:** - $A\to B = N41^\circ35'E$ - $B\to C = 92^\circ24'$ - $C\to D = 183^\circ49'$ - $D\to E = 231^\circ19'$ - $E\to F = 275^\circ37'$ - $F\to A = 336^\circ45'$ These azimuths represent the bearings of each side of the hexagon starting from $A\to B$ and moving clockwise around the polygon.