Problem $4(30$ points$)$

A four$-$sided polygon, ABCD $,$ is measured by a counter$-$clockwise close$-$loop interior angle traverse. The interior angles measured at the points $A,B,C,$ and D are $75{56}^{\text{'}}{00}^{\text{'}\text{'}},107{20}^{\text{'}}{00}^{\text{'}\text{'}},87{30}^{\text{'}}{00}^{\text{'}\text{'}},$ and $89{15}^{\text{'}}{00}^{\text{'}\text{'}},$ respectively. And, the distance of lines $AB,BC,CD,$ and DA are measured as $232\mathrm{.}380m,239\mathrm{.}890m,239\mathrm{.}180m,$ and $299\mathrm{.}330$ m $,$ respectively. Assume that the azimuth of the line AD is given as $234{32}^{\text{'}}{00}^{\text{'}\text{'}},$ and the coordinate of the point A is $(500,500).$

$(1)$ Adjusted Azimuth $(13$ points$)$

AB:

BC:

CD:

$(2)$ Coordinates $(12$ points$)$:

B:

C: $q,$ D: $q,.$

$(3)$ Area of the Polygon: $q,(5$ points$)$