Draw an angle of $80^{\circ}$ with the help of a protractor. Then construct angles of $(i)$ $40^{\circ}$,$(ii)$ $160^{\circ}$,and $(iii)$ $120^{\circ}$.

(N/A) Steps of construction:
$1.$ Draw a ray $OA$.
$2.$ With the help of a protractor,construct $\angle BOA = 80^{\circ}$.
$3.$ Taking $O$ as the center and any suitable radius,draw an arc to intersect rays $OA$ and $OB$ at points $P$ and $Q$ respectively.
$4.$ Bisect $\angle BOA$. Let ray $OC$ be the bisector of $\angle BOA$,then $\angle COA = \frac{1}{2} \angle BOA = \frac{1}{2} \times 80^{\circ} = 40^{\circ}$.
$5.$ With $Q$ as the center and radius equal to $PQ$,draw an arc to cut the extended arc $PQ$ at $R$. Join $OR$ and produce it to form ray $OD$,then $\angle DOA = 2 \angle BOA = 2 \times 80^{\circ} = 160^{\circ}$.
$6.$ Bisect $\angle DOB$. Let $OE$ be the bisector of $\angle DOB$. Then $\angle EOA = \angle EOB + \angle BOA = \frac{1}{2} \angle DOB + \angle BOA = \frac{1}{2}(80^{\circ}) + 80^{\circ} = 40^{\circ} + 80^{\circ} = 120^{\circ}$.