Find the value of x so that f parallel-to g. The diagram is not to scale.A quadrilateral is formed when two segments are drawn connecting line f to line g. Line f is above line g. The segments are angled in opposite directions. The angle formed by the segment on the left and line f is labeled 3 x. The angle formed by the segment on the left and line g is labeled 5 x plus 36.

Answer 1

To find the value of x that makes f parallel to g, we need to determine the relationship between the angles formed by the segments and lines.

Since the lines f and g are parallel, we know that corresponding angles are congruent. Therefore, the angle formed by the segment on the left and line f (labeled 3x) is congruent to the angle formed by the segment on the right and line f.

Similarly, the angle formed by the segment on the left and line g (labeled 5x + 36) is congruent to the angle formed by the segment on the right and line g.

Therefore, we can set up the following equation:

3x = 5x + 36

Subtracting 3x from both sides, we have:

0 = 2x + 36

Subtracting 36 from both sides, we get:

-36 = 2x

Dividing both sides by 2, we find:

-18 = x

Therefore, the value of x that makes f parallel to g is x = -18.