Question
Using a protractor, draw an angle of measure $72^\circ .$ With this angle as given, draw angles of measure $36^\circ $ and $54^\circ .$
✓
Answer
Draw a ray $OA$.
With the help of a protractor, draw an angle $\angle\text{AOB}$ of $72^\circ $.
With a convenient radius and centre at $O,$ draw an arc cutting sides $OA $ and $OB$ at $P$ and $Q,$ respectively.
With $P$ and $Q$ as centres and radius more than half of $PQ,$ draw two arcs cutting each other at $R.$
Join $O$ and $R$ and extend it to $X.$
$ OR$ intersects arc $PQ$ at $C. $
With $C$ and $Q$ as centres and radius more than half of $CQ,$ draw two arcs cutting each other at $T.$
Join $O$ and $T$ and extend it to $Y.$
Now, $OX$ bisects $\angle\text{AOB}$
Therefore, $\angle\text{AOX}=\angle\text{BOX}=\frac{72}{2}=36^{\circ}$
Again, $OY$ bisects $\angle\text{BOX}$
Therefore, $\angle\text{XOY}=\angle\text{BOY}=\frac{36}{2}=18^{\circ}$
Therefore, $\angle\text{AOX}$ is the required angle of $36^\circ $ and $\angle\text{AOY}=\angle\text{AOX}+\angle\text{XOY}=36^{\circ}+18^{\circ}=54^{\circ}$
Therefore, $\angle\text{AOY}$ is the required angle of $54^\circ .$
With the help of a protractor, draw an angle $\angle\text{AOB}$ of $72^\circ $.
With a convenient radius and centre at $O,$ draw an arc cutting sides $OA $ and $OB$ at $P$ and $Q,$ respectively.
With $P$ and $Q$ as centres and radius more than half of $PQ,$ draw two arcs cutting each other at $R.$
Join $O$ and $R$ and extend it to $X.$
$ OR$ intersects arc $PQ$ at $C. $
With $C$ and $Q$ as centres and radius more than half of $CQ,$ draw two arcs cutting each other at $T.$
Join $O$ and $T$ and extend it to $Y.$
Now, $OX$ bisects $\angle\text{AOB}$
Therefore, $\angle\text{AOX}=\angle\text{BOX}=\frac{72}{2}=36^{\circ}$
Again, $OY$ bisects $\angle\text{BOX}$
Therefore, $\angle\text{XOY}=\angle\text{BOY}=\frac{36}{2}=18^{\circ}$
Therefore, $\angle\text{AOX}$ is the required angle of $36^\circ $ and $\angle\text{AOY}=\angle\text{AOX}+\angle\text{XOY}=36^{\circ}+18^{\circ}=54^{\circ}$
Therefore, $\angle\text{AOY}$ is the required angle of $54^\circ .$
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