Given that line f is parallel to line g, find the value of x. The diagram is not to scale.
A trapezoid is shown formed by two parallel lines and two line segments.· Line f is above line g.
· A positively sloped segment is drawn on the left connecting the parallel lines.
· A negatively sloped segment is drawn on the right connecting the parallel lines, · forming the trapezoid.
· The upper left angle of the trapezoid is labeled 3 x.
· The lower left angle of the trapezoid is labeled 6 x plus 45.
(1 point)
Responses
16
16
–15
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.