Answer:
x = 13
y = 24
Step-by-step explanation:
[tex] \because l || m.... (given) \\\\
\therefore (7x - 31)\degree + [63\degree + (5x - 8)\degree]\\ = 180\degree \\(interior \:\angle 's\: on \:same \: side \: of \: || \: sides) \\\\
\therefore (7x - 31)\degree + 63\degree + (5x - 8)\degree = 180\degree\\\\
\therefore (12x - 39)\degree = 180\degree-63\degree\\\\
\therefore (12x - 39)\degree = 117\degree\\\\
\therefore 12x - 39 = 117\\\\
\therefore 12x = 117+39\\\\
\therefore 12x = 156\\\\
\therefore x =\frac{156}{12}\\\\
\huge \orange {\boxed {\therefore x = 13}} \\\\[/tex]
By remote interior angle theorem:
[tex] (4y +27)\degree = (7x - 31)\degree +63\degree \\\\
(4y +27)\degree = (7x +32)\degree \\\\
4y + 27 = 7\times 13 +32\\\\
4y = 91+ 32-27\\\\
4y = 96\\\\
y = \frac {96}{4}\\\\
\huge \purple {\boxed {y = 24}} [/tex]
