Find the value of x that will make A||B.
А
5X
(4x + 12
x
< = [?]

x=12

Step-by-step explanation:

Lines A and B are parallel, with a transversal passing through them.

The properties of two parallel lines and a transversal tells us that angles 5x and 4x+12 must be equal, because they are a pair of alternate exterior angles.

To solve for x, we do 5x=4x+12

Subtract 4x on both sides

x=12

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4