An interior angle $x$ and its explement $y$ were turned to close the horizon. Each angle was observed once direct and once reversed using the repetition method. Starting with an initial backsight setting of $0{00}^{\text{'}}{00}^{\text{'}\text{'}}$ for each angle, the readings after the first and second turnings of angle $x$ were $52{34}^{\text{'}}{47}^{\text{'}\text{'}}$ and $52{34}^{\text{'}}{40}^{\text{'}\text{'}},$ and the readings after the first and second turnings of angle $y$ were $308{20}^{\text{'}}{15}^{\text{'}\text{'}}$ and $308{20}^{\text{'}}{9}^{\text{'}\text{'}}.$ Calculate each angle and the horizon misclosure. $(10$ points$)$