Question

Find m BDC. B C (-3x + 20° { (-2x + 55) ° D А a. 290 b. 61° c. 25° d. 759

Answer 1

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)

`\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 \\ (-5x)/(-5)=(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}`

Hence, option A is the correct answer