Question
Use a pair of compasses and construct the following angles: $105^\circ $
✓
Answer
Steps of Construction:
$1.$Draw a ray $OA.$
$2.$With $O$ as centre and any suitable radius draw an arc cutting $OA$ at $B.$
$3.$With $B$ as centre and same radius cut the previous arc at $C$ and then with $C$ as centre and same radius cut the arc at $D.$
$4.$With $C $ as centre and radius more than half $CD$ draw an arc.
$5.$With $D$ as centre and same radius draw another arc to cut the previous arc at $E.$
$6.$Join $OE.$ Also join $OD$ and produce it to $F.$
$7.$Draw the bisector $OG$ of $\angle\text{EOF}.$
Thus, $\angle\text{AOG}=105^\circ$ is the required angle.
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