Question
Construct the angle with the help of ruler and compasses only:
$45^\circ $
$45^\circ $
✓
Answer
To construct an angle of $45^\circ ,$ construct an angle of $90^\circ $ and bisect it.
Construct the angle $\angle\text{AOB}=90^{\circ},$ where rays $OA$ and $OB$ intersect the arc at points $P$ and $T$ as shown in figure.
With $P$ and $T$ as centres and radius more than half of $PT, $ draw two arcs, which cut each other at $X$
Draw $OX$ and extend it to $C$ to form the ray $OC.$
$\angle\text{AOC}$ is the required angle of $45^\circ .$
Construct the angle $\angle\text{AOB}=90^{\circ},$ where rays $OA$ and $OB$ intersect the arc at points $P$ and $T$ as shown in figure.
With $P$ and $T$ as centres and radius more than half of $PT, $ draw two arcs, which cut each other at $X$
Draw $OX$ and extend it to $C$ to form the ray $OC.$
$\angle\text{AOC}$ is the required angle of $45^\circ .$
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