Which statement allows for us to conclude that line m and line n are parallel?

if ∡3 is a supplementary angle with ∡5, namely they both add up to 180°, then that means that the corresponding angles of ∡1 = ∡5, and ∡3 = ∡7, which means the lines crossing those angles are parallel.

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

idk

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