Question

In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.

Answer 1

We have, two parallelograms ABDH and CEFG.
In parallelogram ABDH,
$\angle ABD+\angle BDH={180}^{\circ }$ [$\because$ adjacent angles of a parallelogram are supplementary]
$\Rightarrow \angle BDH={180}^{\circ }-{130}^{\circ }\Rightarrow \angle BDH={50}^{\circ }\dots \dots \left(i\right)$
In parallelogram CEFG,
$\angle GCE=\angle GFE$ [$\because$Opposite angles are equal]
$\Rightarrow \angle GCE={30}^{\circ }\dots \dots \left(ii\right)$

In $\Delta OCD$, by using angle sum property, $\angle OCD+\angle ODC+\angle COD={180}^{\circ }$
$\Rightarrow {50}^{\circ }+{30}^{\circ }+x={180}^{\circ }$ [From (i) and (ii)]
$\Rightarrow x={180}^{\circ }-{80}^{\circ }={100}^{\circ }$