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
To solve for the value of x, you need to understand that the interior angles on the same side of a trapezoid are supplementary when the trapezoid has one pair of parallel sides, which means that their measures add up to 180 degrees.
Given the information that line f is parallel to line g (forming a trapezoid) and the two angles on the left side of the trapezoid are 3x and 6x + 45, we set up the equation for the supplementary angles:
3x + 6x + 45 = 180
Combine like terms:
9x + 45 = 180
Now, subtract 45 from both sides:
9x = 180 - 45
9x = 135
Divide both sides by 9:
x = 135 / 9
x = 15
So the value of x is 15. The correct answer from the provided choices is:
15