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Construction a quadrilateral $LION$ with $LI=6.5\ cm$, $IO=7.2\ cm$, $\angle I=90^o$, $\angle O = 60^o$ and $\angle N=105^o$.
Given: A quadrilateral $LION$ with $LI=6.5\ cm,\ IO=7.2\ cm,\ \angle I=90^o,\ \angle O = 60^o$ and $\angle N=105^o$.
To do: To construct the quadrilateral $LION$.
Solution:
As given, In quadrilateral $LION$: $LI=6.5\ cm,\ IO=7.2\ cm,\ \angle I=90^o,\ \angle O = 60^o$ and $\angle N=105^o$
$\Rightarrow \angle L +\angle I +\angle O+\angle N=360^o$
$\Rightarrow \angle L+90^o+60^o+105^o=360^o$
$\Rightarrow \angle L+255^o=360^o$
$\Rightarrow \angle L=360^o-255^o$
$\Rightarrow \angle L=105^o$
1. Draw $LI=6.5\ cm$.
2. Draw an angle $\angle XLI=105^o$ at point $L$.
3. Draw an angle $\angle I=90^o$ at point $I$.
4. Take point $I$ as center and draw an arc with radius $7.2\ cm$ which intersects the line at $O$.
5. At $O$, draw an angle $\angle YOI=60^o$.
6. $OY$ intersects $LX$ at $N$
Thus, $LION$ is the required quadrilateral.
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