In a right triangle, the measure of one of the acute angles is 60 degrees more than the measure of the smallest angle. find the measures of all three angles.

90°, 75°, and 15°

Step-by-step explanation:

In a right triangle, one of the angles is 90°.

           Let x = the smallest angle

Then 60 + x = the third angle

The sum of the three angles is 180°.

90 + 60 + x + x = 180

          150 + 2x = 180

                    2x =  30

                      x =   15

      Measure of right angle              = 90°

Measure of smallest angle = x         =  15°

     Measure of third angle = 60 + x = 75°  

The measures of the angles are 90°, 75°, and 15°.