The measure if one acute angle in a right triangle is 1 1/4 times the measure of the other acute angle. what is the measure of the larger acute angle?

In a right triangle:
α + β = 90°
α = 5/4 β 

5/4 β + β = 90°
9/4 β = 90°
β = 90° : 9/4 = 90° · 4/9 = 40°
α = 90° - 40° = 50°

The measure of the larger acute angle is 50°.