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Angles of a triangle

Source: Czech and Slovak Olympiad 1953, National Round, Problem 2

February 15, 2022
geometryanglesTriangle

Problem Statement

Let α,β,γ\alpha,\beta,\gamma be angles of a triangle. Two of them can be expressed using an auxiliary angle φ\varphi in a way that \alpha=\varphi+\frac\pi4, \beta=\pi-3\varphi. Show that α>γ.\alpha>\gamma.
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