Answer:
x = 58
[tex] m\angle 4 = 116\degree [/tex]
Step-by-step explanation:
[tex] m\angle 2 = m\angle 6..... (1)\\(alternate \: \angle s) \\\\
m\angle 5 + m\angle 6 = 180\degree \\(linear \: pair\: \angle s) \\\\
\therefore m\angle 6 = 180\degree-m\angle 5..... (2)\\\\[/tex]
From equations (1) & (2)
[tex] m\angle 2 =180\degree-m\angle 5\\\\
\therefore (2x)\degree =180\degree-(x+6)\degree \\\\
\therefore (2x)\degree +(x+6)\degree =180\degree\\\\
\therefore (2x+x+6) \degree =180\degree\\\\
\therefore (3x+6) \degree =180\degree\\\\
3x + 6 = 180\\\\
3x = 180-6\\\\
3x = 174\\\\
x = \frac{174}{3} \\\\
\huge \purple {\boxed {x = 58}} \\\\
\because m\angle 4 = m\angle 2\\(corresponding \: \angle s) \\\\
\therefore m\angle 4 = (2x)\degree \\\\
\therefore m\angle 4 = (2\times 58)\degree \\\\
\huge \orange {\boxed {\therefore m\angle 4 = 116\degree}} [/tex]
