The two acute angles in a right triangle measure (2x + 7)° and (3x - 2)°. Find x and the measure of the two acute angles.

To find x and the measure of the two acute angles, we can use the fact that the sum of the two acute angles in a right triangle is always 90 degrees.

So, we can set up the equation:
(2x + 7) + (3x - 2) = 90

Now let's solve for x.

Combine like terms:
2x + 7 + 3x - 2 = 90
5x + 5 = 90

Subtract 5 from both sides:
5x = 90 - 5
5x = 85

Divide both sides by 5:
x = 85/5
x = 17

Now that we have found x, we can substitute it back into the expressions for the acute angles:
Angle 1: 2x + 7 = 2(17) + 7 = 34 + 7 = 41°
Angle 2: 3x - 2 = 3(17) - 2 = 51 - 2 = 49°

Therefore, the measure of the two acute angles is 41° and 49°, respectively. And x is equal to 17.