In a right triangle the acute angles measure x plus 15 and 2x degrees. What is the measure of the larger acute angle of the triangle?

The 3 interior angles of a right angle triangle add up to 180 degrees and so:-

If: x+15+2x+90 = 180

Then: 3x = 75 and so x = 25

Therefore the largest acute angle is 2x = 50 degrees

Check: 45+55+90 = 180 degrees