Question
Using your protractor, draw an angle of measure $108^\circ .$ With this angle as given, draw an angle of $54^\circ .$
✓
Answer
Draw a ray $OA.$
With the help of a protractor, construct an angle $\angle\text{AOB}$ of $108^\circ .$
Since, $\frac{108}{2}=54^{\circ}$
Therefore, $54^\circ $ is half of $108^\circ .$
To get the angle of $54^\circ ,$ we need to bisect the angle of $108^\circ .$
With centre at $O$ and a convenient radius, draw an arc cutting sides $OA$ and $OB$ at $P$ and $Q,$ respectively.
With centre at $P$ and radius more than half of $PQ,$ draw an arc.
With the same radius and centre at $Q,$ draw another arc intersecting the previous arc at $R.$
Join $O$ and $R$ and extend it to $X.$
$\angle\text{AOX}$ is the required angle of $54^\circ .$
With the help of a protractor, construct an angle $\angle\text{AOB}$ of $108^\circ .$
Since, $\frac{108}{2}=54^{\circ}$
Therefore, $54^\circ $ is half of $108^\circ .$
To get the angle of $54^\circ ,$ we need to bisect the angle of $108^\circ .$
With centre at $O$ and a convenient radius, draw an arc cutting sides $OA$ and $OB$ at $P$ and $Q,$ respectively.
With centre at $P$ and radius more than half of $PQ,$ draw an arc.
With the same radius and centre at $Q,$ draw another arc intersecting the previous arc at $R.$
Join $O$ and $R$ and extend it to $X.$
$\angle\text{AOX}$ is the required angle of $54^\circ .$
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