I've drawn two random, non-parallel, straight lines on a plane. They cross over, forming two angles, $a$ and $b$, where ($a + b + a + b) = 1$ (or $360^\circ$) and $a ≤ b$. (Making $a$ either the acute angle or a right angle.)
Using only a compass and straight edge, how would I find the value of $a$? It is acceptable to use an infinite number of steps.
(This is an abstract recreational puzzle rather than a practical question. If it were practical, I'd acquire a protractor.)