Question

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
15

14
14

Answer 1

To solve for x, we need to use the fact that the opposite angles of a trapezoid are equal.

Since line f is parallel to line g, the upper left angle of the trapezoid (3x) and the lower right angle of the trapezoid must be equal.

Therefore, we can set up the equation:
3x = 6x + 45

To solve for x, we can subtract 6x from both sides of the equation:
-3x = 45

Then, divide both sides by -3 to solve for x:
x = -15

So the value of x is -15.