∠( 2x + 36 ) and ∠4x are interior angles on the same side of transversal, which means their sum will add up to 180° .
Which means :-
[tex] = 2x + 36 + 4x = 180[/tex]
[tex] = 6x + 36 = 180[/tex]
[tex] = 6x = 180 - 36[/tex]
[tex] = 6x = 144[/tex]
[tex] = x = \frac{144}{6} [/tex]
[tex]\hookrightarrow\color{hotpink} x = \color{hotpink}24[/tex]
To find whether or not we have found out the correct value of x, let us place 24 in the place of x :-
[tex] = 2x + 36[/tex]
[tex] = 2 \times 24 + 36[/tex]
[tex] = 48 + 36[/tex]
[tex]\color{olive}∠(2x + 36) =\color{hotpink} 84°[/tex]
Then :-
[tex] = 4x[/tex]
[tex] = 4 \times 24[/tex]
[tex]\color{olive}∠4x =\color{hotpink} 96°[/tex]
As , the sum of both these angles are adding upto 180° (84+96=180) , we can conclude that we have found out the correct value of x .
Therefore, the value of :-
[tex]\boxed{\color{olive}x \: \:\bold{\color{hotpink} = 24}}[/tex]
