Answer: The required value of x is 11.
Step-by-step explanation: Given that the lines f and g are parallel to each other.
We are to find the value of x.
From the figure, we note that the parallel lines f and g are cut by a transversal, and
angles with measures 5x° and (9x+26)° are interior angles on the same side of the transversal.
We know that, if two lines are parallel, then the measures of the angles on the same side of the transversal is 180°.
Therefore, we get
[tex]5x^\circ+(9x+26)^\circ=180^\circ\\\\\Rightarrow 5x+9x+26=18\\\\\Rightarrow 14x=180-26\\\\\Rightarrow 14x=154\\\\\Rightarrow x=\dfrac{154}{14}\\\\\Rightarrow x=11.[/tex]
Thus, the required value of x is 11.
