Question
Using rulers and compasses only, draw an angle of measure $135^\circ$.
✓
Answer
Steps of construction:
$1.$ Draw a line segment $AB$ and produce $BA$ to $C$.
$2.$ Keeping $A$ as the center and any radius draw an arc which intersects $AC$ at $D$ and $AB$ at $E$.
$3.$ Keeping $D$ and $E$ as center and radius more than half of $DE$ draw arcs which intersect each other at $F$.
$4.$ Join $FA$ which intersects the arc in $(2)$ at $G$.
$5.$ Keeping $G$ and $D$ as center and radius more than half of $GD$ draw arcs which intersect each other at $H$.
$6.$ Join $HA$.
Therefore $\angle\text{HAB}=135^\circ$
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