Question
Construct with ruler and compasses, angles of measure: $30^\circ $
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Answer
The below given steps will be followed to construct an angle of $30^\circ .$
$1.$Draw a line $l$ and mark a point $P$ on it. Now taking $P$ as centre and with convenient radius, draw an arc of a circle which intersects line $l$ at $Q.$
$2.$Taking $Q$ as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point $R.$
$3.$Now, taking $Q$ and $R$ as centre and with radius more than $\frac{1}{2}RQ,$ draw arcs to intersect each other at $S.$ Join $PS$ which is the required ray making $30^\circ $ with line $l.$
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