Question
Construct the angle with the help of ruler and compasses only: $150^\circ $
✓
Answer
Draw a line $AB$ and take point $O$ at the middle of $AB.$
With a convenient radius and centre at $O,$ draw an arc, which cuts the line $AB$ at $P$ and $Q.$
With the same radius and centre at $Q,$ draw an arc, which cuts the first arc at $R.$
With the same radius and centre at $R,$ draw an arc, which cuts the first arc at $S.$
With the centres $P$ and $S$ and radius more than half of $PS,$
draw two arcs, which cut each other at $T.$
Draw $OT$ and extend it to $C$ to form the ray $OC.$
$\angle\text{BOC}$ is required angle of $150^\circ .$
With a convenient radius and centre at $O,$ draw an arc, which cuts the line $AB$ at $P$ and $Q.$
With the same radius and centre at $Q,$ draw an arc, which cuts the first arc at $R.$
With the same radius and centre at $R,$ draw an arc, which cuts the first arc at $S.$
With the centres $P$ and $S$ and radius more than half of $PS,$
draw two arcs, which cut each other at $T.$
Draw $OT$ and extend it to $C$ to form the ray $OC.$
$\angle\text{BOC}$ is required angle of $150^\circ .$
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