Question

In the given figure, AB || CD, $\angle ABO={40}^{\circ }$ and $\angle CDO={30}^{\circ }.$ If $\angle DOB=x,$ then find the value of x.

• A. ${10}^{\circ }$
• B. ${70}^{\circ }$
• C. ${110}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

The correct option is B ${70}^{\circ }$

Through O draw EOE' parallel to AB & so to CD.

$\therefore \angle BO{E}^{\prime }=\angle ABO={40}^{\circ }$ (alternate angles)
$\angle E^{\prime }OD=\angle CDO={30}^{\circ }$ alternate angles)
$\therefore \angle BOD=({40}^{\circ }+{30}^{\circ })={70}^{\circ }.$ So, x = 70.