Please Help me answer these two geometry questions! see attachment

Challenge 4:

x:6 = 5:3 because of parallel lines.

we can write this in fraction form and solve:

x/6=5/3

6(x/6)=6(5/3)

x=30/3=10

5:3=12:y

5/3=12/y

y(5/3)=y(12/y)

5y/3=12

3(5y/3)=3(12)

5y=36

y=36/5

(3a)

Note that angle CBD = angle CBA

And angle   CDB = angle BCA

So....by AA congruency, triangle BDC is similar to triangle BCA

(3b)

Note that angle CAB  =  angle CAD

And angle  ACB = angle  CDA

So....by AA congruency, triangle  ADC  is similar to triangle ACB

For the second one....it's easier to find y first

We have that   

12/5 = y/3      cross- multiply...

3*12 = 5*y 

36 = 5y      divide both sides by 5

36/5 = y = 7.2

And

[12 + 5 ] / x  = [y + 3 ] / 6

[ 17 ] / x = [ 7.2 + 3 ] / 6       cross-multiply

17*6  = 10.2 x  

102 = 10.2 x     divide both sides by 10.2

10 = x