Let's begin by listing out the information given to us:
We will observe that these two angles are complementary (they sum up to 90 degrees)
[tex]\begin{gathered} m\angle BDC=-3x+20 \\ m\angle CDA=-2x+55 \\ m\angle BDC+m\angle CDA=90^{\circ} \\ -3x+20+(-2x+55)=90 \\ \text{Put like term}s\text{ together, we have:} \\ -3x-2x+20+55=90 \\ -5x+75=90 \\ Subtract\text{ 75 from both sides, we have:} \\ -5x+75-75=90-75 \\ -5x=15 \\ \frac{-5x}{-5}=\frac{15}{-5} \\ x=-3 \\ \\ m\angle BDC=-3x+20=-3(-3)+20 \\ m\angle BDC=9+20=29 \\ \therefore m\angle BDC=29^{\circ} \end{gathered}[/tex]
Hence, option A is the correct answer
