Question

Construct a quadrilateral $MORE$ where $MO=6cm$,$OR=4.5cm$ ,$\angle M={60}^o$ , $\angle O={105}^o$ and $\angle R={105}^o$

Also, find the length of side EM (in cm)

Answer 1

$\Rightarrow$ Draw a line segment $MO$ of $6cm$.

$\Rightarrow$ Take $M$ as a center draw an angle of ${60}^o$.

$\Rightarrow$ Take point $O$ as a center draw an angle of ${105}^o$.

$\Rightarrow$ Cut $OR$ at $4.5cm$

$\Rightarrow$ Take $R$ point as a center draw an angle of ${105}^o$.

$\Rightarrow$ The arc of ${105}^o$ angle and the arc of ${60}^o$ angle intersect with each other at $E.$

$\Rightarrow$ Hence, $MORE$ is a required Quadrilateral.

$\Rightarrow$ Now, by using scale measure the length of side $EM$

We get, $EM=7.5cm$