Question

Construct the following quadrilaterals.
Quadrilateral MORE
$MO$=$6cm$
$OR$=$4.5cm$
$\angle M={60}^o$
$\angle O={105}^o$
$\angle R={105}^o$

Answer 1

Here, we are given two adjacent sides and three angles.

Construct the quadrilateral using following steps of construction.

Step I: Draw side $MO$ of length $6cm$.

Step II: Now, draw $60{}^{\circ }$ from point $M$.

Step III: Now, draw $105{}^{\circ }$ from point $O$.

Step IV: Take $4.5cm$ as radius and $O$ as the centre. Draw an arc. The arc intersects the line at point $R$.

Step V: Again, draw $105{}^{\circ }$ from point $R$.

Step VI: Mark point $E$ where the lines from point $M$ and point $R$ intersect. Now, label the sides of the quadrilateral.

Therefore,

$\Rightarrow MORE$ is the required quadrilateral as shown in the figure.