Question
Construct with ruler and compasses, angles of measure: $135^\circ $
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Answer
The below given steps will be followed to construct an angle of $135^\circ .$
$1.$Draw a line l and mark a point $P$ on it. Now taking $P$ as centre and with a convenient radius, draw a semi-circle which intersects line $l$ at $Q$ and $R.$
$2.$Taking $R$ as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at $S.$
$3.$Taking $S$ as centre and with the same radius as before, draw an arc intersecting the arc at $T$ (see figure).
$4.$Taking $S$ and $T$ as centre, draw arcs of same radius to intersect each other at $U.$
$5.$Join $PU.$ Let it intersect the arc at $V.$ Now taking $Q$ and $V$ as centres and with radius more than $\frac{1}{2}$$QV,$ draw arcs to intersect each other at $W.$
$6.$Join PW which is the required ray making $135^\circ $ with line $l.$
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