Question

Find X so that l (double vertical line) m.Show your work.

Answer 1

If l and m are parallel, this means that the angles I'm going to show you in red must be equal:

So what I'm saying is that:

$\alpha=7x+5$

Also, since the angle under alpha and the angle (5x+19) are supplementary:

$\beta+(5x+19)=180º$

And, as you can see, beta and alpha are supplementary too, so:

$\alpha+\beta=180º$

From the second equation we clear beta:

$\beta=180º-(5x+19)$

And we replace it in the equation of beta and alpha. Also, we have to replace alpha with the expression in the first equation:

$\alpha+\beta=(7x+5)º+(180º-(5x+19)º)=180º$

And then, we just clear the x:

I'll take the parenthesis out.

$7x+5+180-5x-19=180$

We group the x and add up the constants:

$(7x-5x)+(5+180-19)=180$$2x+166=180$

166 goes to the other side as a substraction and the 2 goes dividing:

$x=\frac{180-166}{2}$

Finally, the value of x is:

$x=7$