Given a $17^\circ$ angle, construct a $1^\circ$ angle using only a compass and straightedge

$\begingroup$

Given a $17^\circ$ angle, construct a $1^\circ$ angle using only a compass and straightedge

I've tried creating 20 seventeen angles so that there is a $360-20*17=20$ angle left. However, this is not possible as an angle can only be divided into powers of 2.

If we construct 64 seventeen degree angles, we are left an 8-degree angle. This can be bisected three times to achieve a 1-degree angle. Is this an valid construction?

$\endgroup$ 1

3 Answers

$\begingroup$

Note that $17 \times 7 = 119$. Can you construct a $120$-degree angle?

$\endgroup$ $\begingroup$

Construct a 60° angle and bisect twice. Subtract the result (15°) from the given 17° angle and bisect.

$\endgroup$ $\begingroup$

An further possibility would be to construct a regular pentagon by usual means. Subdivide it to obtain a decagon and once more for a icosagon. That one then amounts to a centry-angle of 18 degrees. Subtract your 17 degrees angle therefrom, and you are left with ...?

--- rk

$\endgroup$ 1

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

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