Question

how to draw 150 degree angle using compass

Answer 1

150∘=180∘−30∘=180∘−(12×60∘).150∘=180∘−30∘=180∘−(12×60∘).

180∘180∘ is easy — just a line segment.

60∘60∘ is also easy — the angle in an equilateral triangle. So, the construction is simple.

Bisecting an angle is easy.

Take a line segment, say, ABAB.

Choose a point CC on it.

With center CC, and radius BCBC, draw an arc.

With center BB and radius BCBC, cut the previous arc at say DD. (∠DCB=60∘∠DCB=60∘because we just made CD=BC=BDCD=BC=BD.)

With center DD, and radius BCBC draw an arc.

With center BB and radius BCBC, cut this arc at, say, EE. Then ECEC is the bisector of ∠BCD∠BCD, and hence ∠BCE∠BCE=30∘=30∘.

Then, ∠ACE=180∘−∠BCE=150∘.