$(5$ points$)$ Per the figure, using a total station

placed at A$,$ direct and reversed angles relative

to North $(00^{\text{'}}{0}^{\text{'}\text{'}})$ were collected to points B$,$ C$,$

D$,$ then back to North as shown in the table:

Determine:

$(3$a$)$ the averaged angle of North$-$A$-$B

a$.64{14}^{\text{'}}{57}^{\text{'}\text{'}}$

b$.65{14}^{\text{'}}{57}^{\text{'}\text{'}}$

$(3$b$)$ the averaged angle of North$-$A$-$D

c$.65{14}^{\text{'}}{27}^{\text{'}\text{'}}$

a$.260{58}^{\text{'}}{48}^{\text{'}\text{'}}$

b$.260{58}^{\text{'}}{18}^{\text{'}\text{'}}$

d$.64{14}^{\text{'}}{27}^{\text{'}\text{'}}$

c$.259{58}^{\text{'}}{48}^{\text{'}\text{'}}$

d$.259{58}^{\text{'}}{18}^{\text{'}\text{'}}$

$(3$c$)$ the angle $x(B-A-C)$

$(3$d$)$ the angle $y($C$-$A$-$D$)$

$(3$e$)$ the angle $z($D$-$A$-$B$)$

a$.76{22}^{\text{'}}{22}^{\text{'}\text{'}}$

a$.119{21}^{\text{'}}{29}^{\text{'}\text{'}}$

a$.164{15}^{\text{'}}{49}^{\text{'}\text{'}}$

b$.75{21}^{\text{'}}{52}^{\text{'}\text{'}}$

b$.119{22}^{\text{'}}{59}^{\text{'}\text{'}}$

b$.164{16}^{\text{'}}{09}^{\text{'}\text{'}}$

c$.75{22}^{\text{'}}{52}^{\text{'}\text{'}}$

c$.119{22}^{\text{'}}{29}^{\text{'}\text{'}}$

c$.164{15}^{\text{'}}{09}^{\text{'}\text{'}}$

d$.76{21}^{\text{'}}{22}^{\text{'}\text{'}}$

d$.119{21}^{\text{'}}{59}^{\text{'}\text{'}}$

d$.164{16}^{\text{'}}{49}^{\text{'}\text{'}}$

$(3$f$)$ the theoretical sum of angles $x,y,z$

$(3$g$)$ the horizon misclosure

a$.90{00}^{\text{'}}{00}^{\text{'}\text{'}}$

a$.0{00}^{\text{'}}{08}^{\text{'}\text{'}}$

b$.180{00}^{\text{'}}{00}^{\text{'}\text{'}}$

b$.0{00}^{\text{'}}{05}^{\text{'}\text{'}}$

c$.360{00}^{\text{'}}{00}^{\text{'}\text{'}}$

c$.0{00}^{\text{'}}{07}^{\text{'}\text{'}}$

d$.540{00}^{\text{'}}{00}^{\text{'}\text{'}}$

d$.0{00}^{\text{'}}{01}^{\text{'}\text{'}}$

$(5$ points $-1$ each for $(3a),(3b),$ and $)$ and $\frac{1}{2}$ each for $(3$c$),(3$d$),(3$e$),$ and $(3$f$))$