What is the value of x?
A pair of intersecting lines is shown. The angle above the point of intersection is labeled left parenthesis 7 x minus 8 right parenthesis degrees. The angle directly opposite below the point of intersection is labeled left parenthesis 6 x plus 11 right parenthesis degrees.
(1 point)
Responses
–19
–19
125
125
19
19
55
55
The angle above the point of intersection is equal to the angle directly opposite below the point of intersection since they are vertical angles. Therefore, we can set up the following equation:
7x - 8 = 6x + 11
Subtracting 6x from both sides, we get:
7x - 6x - 8 = 11
Simplifying, we get:
x - 8 = 11
Adding 8 to both sides, we get:
x = 19
Therefore, the value of x is 19.
To find the value of x, we need to set the two given angles equal to each other since they are opposite angles when two lines intersect.
We have:
7x - 8 = 6x + 11
Now, let's solve for x.
First, we can simplify the equation by moving the constants to one side and the variables to the other side:
7x - 6x = 11 + 8
Simplifying further:
x = 19
Therefore, the value of x is 19.