Balance the following interior angles$-$to$-$the$-$right for a polygon traverse to the nearest $1^{\text{'}\text{'}}.$ Compute the azimuths assuming a fixed azimuth of $277{00}^{\text{'}}{04}^{\text{'}\text{'}}$ for line AB$.$

$A=119{37}^{\text{'}}{10}^{\text{'}\text{'}}$;$B=106{12}^{\text{'}}{58}^{\text{'}\text{'}}$;$,C=104{39}^{\text{'}}{22}^{\text{'}\text{'}}$;

$D=130{01}^{\text{'}}{54}^{\text{'}\text{'}}$;$E=79{28}^{\text{'}}{16}^{\text{'}\text{'}}.($ Note: Line $BC$ bears $SW.)$