Question
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.
(1 point)
Responses
19
19
18
18
17
17
–18
–18
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To determine the value of x so that f is parallel to g, we need to find the angle relationship between the angles formed by the two segments and lines f and g.
According to the given information, the angle formed by the segment on the left and line f is labeled 3x, and the angle formed by the segment on the left and line g is labeled 5x + 36.
For f to be parallel to g, these two angles must be corresponding angles. Corresponding angles are equal when two parallel lines are intersected by a transversal.
So, we can set up an equation:
3x = 5x + 36
To solve this equation, we can simplify it:
-2x = 36
Dividing both sides of the equation by -2:
x = -18
Therefore, the value of x that makes f parallel to g is -18.
To find the value of x so that line f is parallel to line g, we need to use the property that when a transversal cuts two parallel lines, the corresponding angles are equal.
In this case, the corresponding angles are 3x (angle formed by the segment on the left and line f) and 5x + 36 (angle formed by the segment on the left and line g).
Since the lines are parallel, the corresponding angles must be equal. Therefore, we can set up the following equation:
3x = 5x + 36
To solve for x, we need to isolate the variable. Let's subtract 5x from both sides of the equation:
3x - 5x = 5x + 36 - 5x
-2x = 36
Now, divide both sides of the equation by -2:
(-2x) / -2 = 36 / -2
x = -18
So, the value of x that makes line f parallel to line g is -18.