Find the measures of the angles of a right triangle where one of the two acute angles measure 5 times the other

Since it is a right angle, you know that the angle measures 90 degrees. Since one acute angle measures 5x (times) the other, you would set it up in equation format as 5x + x = 90.

5x + x = 6x, so
6x = 90
you divide both both sides by 6 (90/6) = 15

To find the measure of the angle that is 5x (times) the other, you do 5(15) = 75 degrees and the other angle is 15 degrees, which adds up to 90 degrees.