2. The measures of the external angles of a right triangle (which are not right) are in the ratio $7: 11$. Determine the measures of the acute angles of that triangle.
First method: In a right-angled triangle, one of the exterior angles is a right angle. Let $\alpha_{1}$ and $\beta_{1}$ be the measures of the remaining two exterior angles of the triangle.

The sum of the measures of the exterior angles of a triangle is $360^{\circ}$, so we have:

$\alpha_{1}+\beta_{1}+90^{\circ}=360^{\circ}$, or $\alpha_{1}+\beta_{1}=270^{\circ}$.

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Since $\alpha_{1}: \beta_{1}=7: 11$, there exists a rational number $k$ such that $\alpha_{1}=7k$ and $\beta_{1}=11k$.

Then $7k + 11k = 270^{\circ}$

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$18k = 270^{\circ}$

$k = 15^{\circ}$

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Then $\alpha_{1} = 7 \cdot 15 = 105^{\circ}$

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So $\alpha = 180^{\circ} - 105^{\circ} = 75^{\circ}$,

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and the angle $\beta = 90^{\circ} - 75^{\circ} = 15^{\circ}$.