Question

In the adjoining figure, it is given that AB || CD, ∠AOB = 50° and ∠CDO = 40°.
Find the measure of ∠BOD.

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{AB}\parallel \hspace{0.17em}\mathrm{CD} \\ \angle \mathrm{ABO}=50° \\ \angle \mathrm{CDO}=40° \\ \mathrm{Construction}:\mathrm{Through}\mathrm{O},\mathrm{draw}\mathrm{EOF}\parallel \mathrm{AB}. \\ \angle \mathrm{ABO}=\angle \mathrm{BOF}=50°(\mathrm{alternate}\mathrm{angles},\mathrm{when}\mathrm{AB}\parallel \mathrm{EF}\mathrm{and}\mathrm{OB}\mathrm{is}\mathrm{a}\mathrm{transversal}) \\ \angle \mathrm{FOD}=\angle \mathrm{ODC}=40°(\mathrm{alternate}\mathrm{angles},\mathrm{when}\mathrm{CD}\parallel \mathrm{EF}\mathrm{and}\mathrm{OD}\mathrm{is}\mathrm{a}\mathrm{transversal}) \\ \angle \mathrm{BOD}=\angle \mathrm{BOF}+\angle \mathrm{FOD} \\ \angle \mathrm{BOD}=50°+40°=90° \end{gathered}$$