Given l || m, m<9 = 9x + 5, and m<5 = x+ 37, find the value of x
To find the value of x, we need to use the information given in the problem:
1. We know that lines l and m are parallel, which means they have the same slope.
2. We are given the equations of two angles, m<9 and m<5, in terms of x.
First, let's find the slope of line m using the information from m<9.
The given equation for m<9 is m<9 = 9x + 5.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope.
Comparing this form with the equation for m<9, we see that the coefficient of x is the slope (m). So, in this case, the slope of line m is 9.
Since l || m, lines l and m have the same slope. Therefore, the slope of line l is also 9.
Now, let's find the value of x by equating the equations of m<9 and m<5:
m<9 = m<5
(9x + 5) = (x + 37)
Simplifying this equation, we have:
9x + 5 = x + 37
Subtracting x from both sides:
8x + 5 = 37
Subtracting 5 from both sides:
8x = 32
Dividing both sides by 8:
x = 4
Therefore, the value of x is 4.