Question

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

Answer 1

In the figure,

AB and CD intersect at O

and $AC\left|\right|DB,\angle CAB={45}^{\circ }$

and $\angle CDB={55}^{\circ }$

$\because AC\left|\right|DB$
$\therefore \angle CAB=\angle ABD$ (Alternate angles)
In $\Delta OBD,$
$\angle BOD={180}^{\circ }-(\angle CDB+\angle ABD)$
=${180}^{\circ }-({55}^{\circ }+{45}^{\circ })$
=${180}^{\circ }-{100}^{\circ }={80}^{\circ }$