Question
In the adjoining figure, it is given that AB || CD, $\angle\text{ABO}=50^\circ$ and $\angle\text{CDO}=40^\circ.$ Find the measure of $\angle\text{BOD}.$
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Answer
Given: AB || CD$\angle\text{ABO}=50^\circ$$\angle\text{CDO}=40^\circ$
Construction: Through O, draw EOF || AB.$\angle\text{ABO}=\angle\text{BOF}=50^\circ$ (alternate angles, when AB || EF and OB is a transversal)
$\angle\text{FOD}=\angle\text{ODC}=40^\circ$ (alternate angles, when CD || EF and OD is a transversal)
$\angle\text{BOD}=\angle\text{BOF}+\angle\text{FOD}$
$\angle\text{BOD}=50^\circ+40^\circ=90^\circ$
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