Answer:
x = 9, y = 41
Step-by-step explanation:
[tex]\because m\angle ABC = 90\degree \\
\therefore m\angle ABD+m\angle DBC = 90\degree \\
\therefore (3x+7)\degree + (5x+11)\degree = 90\degree \\
\therefore (8x + 18)\degree = 90\degree \\
8x + 18 = 90\\
8x = 90-18\\
8x = 72\\
x = \frac{72}{8}\\
\huge \red {\boxed {x = 9}} \\\\
m\angle DBC + m\angle FBC = 180\degree \\(straight \: line \: \angle 's) \\
(5x + 11)\degree + (3y+1)\degree = 180\degree \\
(5\times 9+11)\degree + (3y+1)\degree = 180\degree \\
(45+11)\degree + (3y+1)\degree = 180\degree \\
56\degree + (3y+1)\degree = 180\degree \\
(3y+1)\degree = 180\degree - 56\degree \\
(3y+1)\degree = 124\degree \\
3y + 1 = 124\\
3y = 123\\
y = \frac {123}{3}\\
\huge \purple {\boxed {y = 41}}
[/tex]
