Adventitious angles problem: the lonely fractional derived angle

Abstract

In the "classical" adventitious angle problem, for a given set of three angles $a$, $b$, and $c$ measured in integral degrees in an isosceles triangle, a fourth angle $\hat{I}¸$ (the derived angle), also measured in integral degrees, is sought. We generalize the problem to find $\hat{I}¸$ in fractional degrees. We show that the triplet $(a,b,c)=(45^{\circ },45^{\circ },15^{\circ })$ is the only combination that leads to $\hat{I}¸=7{\frac{1}{2}}^{\circ }$ as the fractional derived angle.