To find the value of \( x \), we can use the fact that the interior angles on the same side of the transversal of two parallel lines are supplementary—that is, they add up to 180 degrees.
In this case, the two angles at the left side of the trapezoid are the upper left angle labeled \( 3x \) and the lower left angle labeled \( 6x + 45 \). Since these angles are on the same side of a transversal and formed by the parallel lines, they add up to 180 degrees.
So the equation we can set up is:
\( 3x + 6x + 45 = 180 \)
Combining like terms, we get:
\( 9x + 45 = 180 \)
Next, we subtract 45 from both sides of the equation to isolate the term with \( x \):
\( 9x = 180 - 45 \)
\( 9x = 135 \)
Finally, divide both sides by 9 to solve for \( x \):
\( x = \frac{135}{9} \)
\( x = 15 \)
Therefore, the value of \( x \) is 15.