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
–15
15
To solve for the value of x, we must use the fact that the sum of the angles at any point on a straight line is 180 degrees. Since line f is parallel to line g, we can also conclude that the interior angles on the same side of the transversals formed by the non-parallel sides of the trapezoid are supplementary. In other words, the upper left angle and the lower left angle of the trapezoid must add up to 180 degrees because they are adjacent angles on a straight line.
We can set up the following equation based on the information given:
3x + (6x + 45) = 180
First, combine like terms:
9x + 45 = 180
Now, subtract 45 from both sides to isolate the term with x:
9x = 180 - 45
9x = 135
Finally, divide both sides by 9 to solve for x:
x = 135 / 9
x = 15
Therefore, the value of x is 15.