Adventitious angles problem: the lonely fractional derived angle

TL;DR

This paper generalizes the classical adventitious angle problem to fractional degrees, identifying a unique triplet that yields a specific fractional derived angle in an isosceles triangle.

Contribution

It extends the classical problem to fractional degrees and proves the uniqueness of a specific triplet producing a fractional derived angle.

Findings

The triplet (45°, 45°, 15°) uniquely leads to a 7.5° fractional derived angle.

The problem is generalized from integral to fractional degrees.

The paper establishes the uniqueness of this triplet for the 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 $\theta$ (the derived angle), also measured in integral degrees, is sought. We generalize the problem to find $\theta$ in fractional degrees. We show that the triplet $(a, b, c) = (45^\circ, 45^\circ, 15^\circ)$ is the only combination that leads to $\theta = 7\frac{1}{2}^\circ$ as the fractional derived angle.