The value of [tex]x[/tex] that satisfies all the expressions of the system of linear equations is 20.
Procedure - Determination of a variable associated to a pair of corresponding angles
According to the figure, angles 1 and 5 are corresponding angles between two parallel lines, therefore we have the following equivalence:
[tex]4\cdot x + 40 = 120[/tex] (1)
After some algebraic handling we find the value of [tex]x[/tex]:
[tex]4\cdot x = 80[/tex]
[tex]x = 20[/tex]
The value of [tex]x[/tex] that satisfies all the expressions of the system of linear equations is 20. [tex]\blacksquare[/tex]
Remarks
There is a missing figure for the statement, we proceed to include it below after some research.
To learn more on angles, we kindly invite to check this verified question: https://brainly.com/question/15767203
