x = 1
Answer:
[tex] m\angle XVW = 100\degree[/tex]
Step-by-step explanation:
In the first figure, FP is the bisector of [tex] \angle DFE[/tex]
[tex] \therefore m\angle 1 = m\angle 2\\
\therefore 44x + 1 = 46x - 1\\
\therefore 1 + 1 = 46x - 44x\\
\therefore 2 = 2x\\
\therefore \frac{2}{2} = x \\
\huge \red {\boxed {\therefore x = 1}} [/tex]
In the second figure, VP is the bisector of [tex] \angle XVW[/tex]
[tex] \therefore m\angle 1 = m\angle 2\\
\therefore 12x + 2 = 11x +6\\
\therefore 12x - 11x = 6 - 2\\
\therefore x = 4\\
\because m\angle XVW = m\angle1 + m\angle 2\\
\therefore m\angle XVW = 12x + 2 + 11x +6\\
\therefore m\angle XVW = 23x + 8\\
\therefore m\angle XVW = 23\times 4+ 8\\
\therefore m\angle XVW = 92+ 8\\
\huge \purple {\boxed {\therefore m\angle XVW = 100\degree}} \\
[/tex]
