Please help with this geometry math problem!

∠8 * 4 = ∠7 (1)

∠8 + ∠7 = 180 (2)

Taking the value of ∠7 from (1) and using it in (2):

∠7 = 4 * ∠8

∠8 + ∠7 = 180

∠8 + (4 * ∠8) = 180

∠8 + 4∠8 = 180

5∠8 = 180

∠8 = 36° (3)

Using the value of ∠8 from (3) in (2):

∠8 + ∠7 = 180

36 + ∠7 = 180

∠7 = 144°       and       ∠8 = 36°

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

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