○=> Correct option :
[tex]\color{plum}\bold{(A) \: 37}[/tex]
○=> Steps to derive correct option :
Angle (4x+2)° and angle 150° are vertically opposite angles so, their measures will be equal.
Which means :
[tex] =\tt 4x + 2 = 150[/tex]
[tex] =\tt 4x = 150 - 2[/tex]
[tex] = \tt4x = 148[/tex]
[tex] =\tt x = \frac{148}{4} [/tex]
[tex]\hookrightarrow \: \color{plum}x = 37[/tex]
Let us check whether or not we have found out the correct measure of x by placing 37 in the place of x:
[tex] =\tt 4 \times 37 + 2 = 150[/tex]
[tex] = \tt148 + 2 = 150[/tex]
[tex] =\tt 150 = 150[/tex]
Since the measures of both the angles are equal we can conclude that we have found out the correct value of x.
Thus, the value of x in this figure = 37
Therefore, the correct option is (A) 37.
