∠4x + 29° and angle ∠12x + 55° are interior angles on the same side of transversal . Which means their sum will be equal to 180° .
We can write this in an equation and solve it as :-
[tex]\mapsto4x + 29 + 12x + 55 = 180[/tex]
[tex]\mapsto \:16x + 29 + 55 = 180[/tex]
[tex]\mapsto16x + 84 = 180[/tex]
[tex]\mapsto16x = 180 - 84[/tex]
[tex]\mapsto16x = 96[/tex]
[tex]\mapsto \: x = \frac{96}{16} [/tex]
[tex]\mapsto\color{darkorange} \: x = 6[/tex]
Let us check whether or not we have found out the correct value of x , by placing 6 in the place of x .
So :-
∠4x + 29° :-
[tex] = 4 \times 6 + 29[/tex]
[tex] = 24 + 29[/tex]
[tex] \color{red}= 53°[/tex]
∠12x + 55° :-
[tex] = 12 \times 6 + 55[/tex]
[tex] = 72 + 55[/tex]
[tex]\color{teal} = 127°[/tex]
As , 53° + 127° = 180° , we can conclude that we have found out the correct value of x .
Therefore , the value of :-
[tex]\color{green}x = 6[/tex]
