Question
Construct the angle with the help of ruler and compasses only: $90^\circ $
✓
Answer
Draw a ray $OA.$
With a convenient radius and centre at $O,$
draw an arc cutting the ray $OA$ at $P.$
With the same radius and centre at $P,$
draw another arc, which cuts the first arc at $Q.$
With the same radius and centre at $Q,$ draw another arc,
which cuts the first arc at $R.$
With $Q$ and $R$ as centres and radius more than half of $QR,$
which cuts each other at $S.$
Draw $OS$ and extend it to $B$ from the ray $OB.$
$\angle\text{AOB}$ is required angle of $90°.$
With a convenient radius and centre at $O,$
draw an arc cutting the ray $OA$ at $P.$
With the same radius and centre at $P,$
draw another arc, which cuts the first arc at $Q.$
With the same radius and centre at $Q,$ draw another arc,
which cuts the first arc at $R.$
With $Q$ and $R$ as centres and radius more than half of $QR,$
which cuts each other at $S.$
Draw $OS$ and extend it to $B$ from the ray $OB.$
$\angle\text{AOB}$ is required angle of $90°.$
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