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

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.

• 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. Jul 16 '20 at 3:23
• thank you very much, @mr_e_man Jul 16 '20 at 3:29
• @mr_e_man You should make this an answer. Jul 17 '20 at 13:29