Line segments AB and CD intersect at O such that AC || DB. If =45… - Vidyadip

Question

Line segments AB and CD intersect at O such that AC || DB. If $\angle\text{CAB}=45^\circ$ and $\angle\text{CDB}=55^\circ,$ then $\angle\text{BOD}=$

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Answer

80º
Solution:

AC || BD
And, AB is transverse to these parallal lines
So $\angle\text{CAB}=\angle\text{ABD}$ (Alternate angles)
$\Rightarrow\angle\text{ABD}=45^\circ$
Now In $\triangle\text{BOD}$
$\angle\text{BOD}+\angle\text{ODB}+\angle\text{DBA}=180^\circ$
$\angle\text{DBA}=\angle\text{ABD}=45^\circ,\angle\text{ODB}=55^\circ$
So $\angle\text{BOD}=180^\circ-45^\circ-55^\circ$
$=80^\circ$

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