$(50$ pts $)$ For the traverse survey shown below and using the field measurements labeled in the figure. The azimuth for line AE N $58{52}^{\text{'}}{48}^{\text{'}\text{'}}E.$

a$.(5$ pts$)$ Determine the angular misclosure.

b$.(5$ pts$)$ Balance the aingles.

c$.(10$ pts$)$ Calculate the$-$Azimuths of all the lines.

d$.(10$ pts$)$ Calculate the departures and latitudes for all the lines.

e$.(10$ pts$)$ Calculate the linear misclosure.

f$.(10$ pts$)$ Adjust the lengths of each line using the compass rule.

Use $3$ decimals for the departure and latitudes as well as the adjusted lengths.