Answer
$\overline{AB}$$\parallel$$\overline{CD}$
Work Step by Step
$\angle$A corresponds to $\angle$C, so 3x+18=4x.
1. 3x+18=4x (subtract 3x from both sides.)
......... 18=x
Check: $\angle$A=3$\times$18+18 = 54+18 = 72
and $\angle$C=4$\times$18=72
2. Since $\angle$A corresponds to $\angle$C, then $\angle$B will correspond to $\angle$D.
Now we have to find out what $\angle$B equals. Because $\angle$A and $\angle$B are on a line and a line always equals 180 degrees and we already know that $\angle$A equals 72$^{\circ}$, then we do 180-72=$\angle$B. 180-72=108. Now we solve for $\angle$D or 3x.
108=3x (divide 3 from both sides.)
36=x
Check: $\angle$B=108
$\angle$D=3$\times$36 = 108
3. If you look at the image. $\angle$B is not a right angle and neither is $\angle$D. We need to use the other side. So 180-108=72. So $\angle$B and $\angle$D both equal 72$^{\circ}$.
4. Lastly, we need to solve for $\angle$F. The way we do that is by using the Triangle Sum Theorem. The Triangle Sum Theorem means that all three of the interior angles add up to equal 180$^{\circ}$.
Since we know what $\angle$C and $\angle$D equal, we can find out what $\angle$F equals.
We would do 180-($\angle$C+$\angle$D)=$\angle$F.
180-(72+72)=$\angle$F
180-144=36
Check: $\angle$C+$\angle$D+$\angle$F=180$^{\circ}$
72+72+36 = 144+36 = 180$^{\circ}$
