Final answer:
The measures of the acute angles in the right triangle are 56 degrees and 34 degrees when the expressions provided are solved with respect to x.
Step-by-step explanation:
To find the measure of each acute angle in a right triangle labeled 19x - 1 degrees and 13x - 5 degrees, we use the fact that the sum of the angles in a triangle is 180 degrees, and in a right triangle, one angle is always 90 degrees. Therefore, the other two angles (the acute angles) must add up to 90 degrees:
19x - 1 + 13x - 5 = 90
Combining like terms gives us:
32x - 6 = 90
Adding 6 to both sides:
32x = 96
Now divide both sides by 32:
x = 3
Substitute x back into the expressions for each acute angle:
First angle: 19x - 1 = 19(3) - 1 = 57 - 1 = 56 degrees
Second angle: 13x - 5 = 13(3) - 5 = 39 - 5 = 34 degrees
The measures of the acute angles are 56 degrees and 34 degrees, respectively.