The given two angles are called vertically opposite angles which are generally equal.
(Vertically opposite angles are those angles which are opposite to each other when two lines cross)
So,
[tex]3x + 178 = 6x + 238[/tex]
[tex]3x - 6x = 238 - 178 = 60[/tex]
[tex] - 3x = 60[/tex]
[tex] - x = \frac{60}{3} = 20 [/tex]
[tex]x = - 20[/tex]
Now, for verification,
3x+178° = 3(-20) +178° = 118°
6x+238= 6(-20)+238° =118°
