Question
Using ruler and compasses only, draw an angle of measure $135^\circ .$
✓
Answer
We draw a line $AB$ and mark a point $O$ on it. With a convenient radius and centre at $O,$ draw an arc $PQ$ with the help of a compass intersecting the line $AB$ at $P$ and $Q.$ With the same radius and centre at $P,$ draw another arc intersecting the arc $PQ$ at $R.$ With the same radius and centre at $Q,$ draw one more arc intersecting the arc $PQ$ at $S,$ opposite to $P.$ Taking $S$ and $R$ as centres and radius more than half of $SR,$ draw two arcs intersecting each other at $T.$ Join $O$ and $T$ intersecting the arc $PQ$ at $C$. Taking $C$ and $Q$ as centres and radius more than half of $CQ,$ draw two arcs intersecting each other at $D.$ Join $O$ and $D$ and extend it to $X$ to form the ray $OX.$
$\angle\text{AOX}$ is the required angle of measure $135^\circ .$
$\angle\text{AOX}$ is the required angle of measure $135^\circ .$
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