Question

In the given figure, AB || CD and O is a point joined with B and D, as shown in the figure, such that ∠AOB = 35° and ∠CDO = 40°. What will be the measure of reflex ∠BOD ?
(a) 225°
(b) 265°
(c) 275°
(d) 285°

Answer 1

(d) 285°

Draw $EOF\parallel AB\parallel CD$.
Now, $EF\parallel AB\text{and}OB$ is the transversal.
$$\begin{gathered} \therefore \angle ABO+\angle EOB=180°\left[\text{Angles on the same side of a transversal line are supplementary}\right] \\ \Rightarrow 35°+\angle EOB=180° \\ \Rightarrow \angle EOB=145° \end{gathered}$$
Also,
$EF\parallel CD$ and OD is the transversal.
$$\begin{gathered} \therefore \angle CDO+\angle EOD=180°\left[\text{Angles on the same side of a transversal line are supplementary}\right] \\ \Rightarrow 40°+\angle EOD=180° \\ \Rightarrow \angle EOD=140° \end{gathered}$$
Therefore,
$$\begin{gathered} \text{Reflex}\angle BOD=\angle EOB+\angle EOD \\ \Rightarrow \angle BOD=\left(145+140\right)° \\ \Rightarrow \angle BOD=\mathbf{285}\mathbf{°} \end{gathered}$$