Question

In the adjoining figure, it is given that AB is parallel to CD,

$\angle ABO={50}^{\circ }$ and $\angle CDO={40}^{\circ }$.

Find the measure of $\angle BOD$ .

• A. $100$
• B. $110$
• C. $90$
• D. $80$

Answer 1

The correct option is C $90$

$AB\parallel CD$ [ Given ]

$\angle ABO={50}^o$ [ Given ]

$\angle ODC={40}^o$ [ Given ]

Draw a line $l$ such that,

$AB\parallel EF\parallel CD$

$AB\parallel EF$ and $BO$ is a tranversal.

$\therefore$ $\angle ABO=\angle BOE$ [ Alternate angle ]

$\therefore$ $\angle BOE={50}^o$

$EF\parallel CD$ and $OD$ is transversal.

$\therefore$ $\angle EOD=\angle CDO$ [ Alternate angle ]

$\therefore$ $\angle EOD={40}^o$

$\Rightarrow$ $\angle BOD=\angle BOE+\angle EOD={50}^o+{40}^o$

$\therefore$ $\angle BOD={90}^o$