please help thank you :)

∠7 = 85°

Step-by-step explanation:

∠1 = 180 - 115 = 65°              Because they are supplementary angles

∠2 = 180 - 65 - 85 = 30°      Because the sum of all interior angles in a triangle

                                             equals 180°

∠3 = 90°                               given

∠6 = 180 - 90 - 30 = 60°      Because they are supplementary angles

∠4 = 180 - 155 = 25°             Because they are supplementary angles

∠5 = 180 - 25 - 60 = 95°      Because the sum of all interior angles in a

                                             triangle equals 180°

∠7 = 180 - 95 = 85°              Because they are supplementary angles

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