Lines l, m, and n are parallel. what is the value of x? ° parallel lines labeled, top to bottom, l, m, and n. a transversal forms a forty-six degree angle that lies to left of the transversal and above line l and an angle with x degrees that is to right of transversal and above line n.

a

step-by-step explanation:

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