Gaiyerin G.A.

The largest angle of an acute triangle is five times the smallest.

Find the angles of this triangle, given that they are all expressed in whole degrees.

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Let $\alpha \geq \beta \geq \gamma$ be the angles of a triangle, and $\alpha=5 \gamma<90^{\circ}$. Then $180^{\circ}=\alpha+\beta+\gamma \leq 5 \gamma+5 \gamma+\gamma=11 \gamma$. Therefore, $180^{\circ}: 11=16^{4} / 11^{\circ} \leq \gamma<90^{\circ}: 5=18^{\circ}$, and since $\gamma$ is expressed in whole degrees, $\gamma=17^{\circ}$.

## Answer

$17^{\circ}, 78^{\circ}, 85^{\circ}$.