Find the angle between parallel lines

Question

I am trying to solve the following problem.
Given: $$\overleftrightarrow{AB} \parallel \overleftrightarrow{DE}$$ And the measures of angles $$\angle BAC = 42 ^{\circ}$$ $$\angle EDC= 54 ^{\circ}$$ Find the measure of angle $$\angle ACD$$ How would you approach to solve the problem. I have tried as recommended on book to assume that there is one parallel line passing through point $C$, but i couldn't produce an answer. What is your advice?
Attached follows the geometric representation

Answer 1

There is a line perpendicular to $AB$ and $DE$ passing through $C$. Say this line meets $AB$ at $X$ and $DE$ at $Y$. Then using the two right-angled triangles, $\angle ACX=90-42=48^{\circ}$ and $\angle DCY=90-54=36^{\circ}$. Since angles on a straight line sum to $180^{\circ}$, $\angle ACD=180-48-36=96^{\circ}$.