Can we construct $142$ degrees and $172$ degrees by using only straightedge and compass?

I already tried rewrite $142$ to get some angles that can be constructed , such as $90$,$45$,$60$,$30$,$15$,$12$ and all multiples of these numbers. But, I still can't construct it. Any hints? Thank you.

  • 13
    $\begingroup$ No. Since angles can be added, subtracted, and halved, and all multiples of $3^\circ$ are constructible, if $142^\circ$ were constructible, then also $$142^\circ-47*3^\circ=1^\circ$$ and thus $140^\circ$ (for example) would be constructible. But we know that the regular $9$-gon is not constructible. $\endgroup$
    – mr_e_man
    Jul 16 '20 at 3:23
  • $\begingroup$ thank you very much, @mr_e_man $\endgroup$
    – dark.nes_s
    Jul 16 '20 at 3:29
  • $\begingroup$ @mr_e_man You should make this an answer. $\endgroup$
    – PrudiiArca
    Jul 17 '20 at 13:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.