Question

Question 9
In the figure, both RISK and CLUE are parallelograms. Find the value of x.

Answer 1

In parallelogram RISK,
$\angle RIS=\angle K={120}^{\circ }$
[Opposite angles of a II gm are equal]
$\angle m+{120}^{\circ }={180}^{\circ }\left[Linearpair\right]$
$\Rightarrow \angle m={180}^{\circ }-{120}^{\circ }={60}^{\circ }$
$And\angle ECI=\angle L={70}^{\circ }\left[Correspondingangles\right]$
$\Rightarrow m+n+\angle ECI={180}^{\circ }\left[Anglesumpropertyofatriangle\right]\Rightarrow {60}^{\circ }+n+{70}^{\circ }={180}^{\circ }\Rightarrow {130}^{\circ }+n={180}^{\circ }\Rightarrow n={180}^{\circ }-{130}^{\circ }={50}^{\circ }Alsox=n={50}^{\circ }\left[Verticallyoppositeangles\right]$