Question
Construct an angle of $90^\circ $ and bisect it.
✓
Answer
Construction steps:
$1.$Draw a line $OA.$
$2.$Take a point $B$ on $OA$. With $B$ as the centre and any convenient radius, draw an arc cutting $OA $ at $M$ and $N.$
$3.$With $N$ as the centre and radius more than half of $MN,$ draw an arc.
$4.$With $M$ as the centre and the same radius as before, draw another arc to cut the previous arc at $W.$
$5.$Draw $WB,$ meeting the arc at $S.$ Produce it to $C.$
$\angle\text{ABC}$ is the required angle of $90^\circ \angle\text{ABC}$ is the required angle of $90^\circ .$
$6.$With $S$ as the centre and radius more than half of $SN,$ draw an arc.
$7.$With $N$ as centre and the same radius as in step $(6),$ draw another arc, cutting the previously drawn arc at point $X.$
$8.$Draw $BX$ and produce it to point $D.$ Ray $BD$ is the angle bisctor of $\angle\text{ABC}.$ Ray $BD$ is the angle bisctor of $\angle\text{ABC}.$ Ray $BD$ is the angl bisctor of $\angle\text{ABC}.$ Ray $BD$ is the angle bisctor of $\angle\text{ABC}.$
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