The ratio of the measures of the acute angles of a right triangle is $8:1$. In degrees, what is the measure of the largest angle of the triangle?
The actual degree measures of the acute angles don't matter. A right triangle consists of a right angle of $90^\circ$ and two acute angles that add up to $90^\circ$, so each of the two acute angles is smaller than the right angle. Also recall that the definition of an acute angle is that its degree measure is less than $90^\circ$. So the largest angle of the triangle is the right angle, which has a measure of $\boxed{90^\circ}$.
90
Level 3
Prealgebra
Problem: The ratio of the measures of the acute angles of a right triangle is $8:1$. In degrees, what is the measure of the largest angle of the triangle?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>In a right triangle, one angle measures 90 degrees. The other two angles are acute and must sum to 90 degrees since the total sum of angles in any triangle is 180 degrees. Given the ratio of the acute angles is 8:1, we can denote the measures of these angles as 8x and x. 

To find the values of these angles, we set up the equation: 8x + x = 90. This simplifies to 9x = 90. Dividing both sides by 9 gives us x = 10. Therefore, the measures of the acute angles are 8x = 80 degrees and x = 10 degrees.

The largest angle in a right triangle is always the right angle, which measures 90 degrees. Thus, the measure of the largest angle of the triangle is 90.<|END_OF_LATENT|> The final answer is $90$.