If the measure of one angle of a right triangle is 30° more than the measure of the smallest angle, then the measure of the smallest angle is:

The correct option is 30°.

Let the smallest angle of the right triangle be represented by $x$.

Since it is a right triangle, one of the three angles is always a right angle, which measures $90°$.

We are given that the measure of one of the other angles is $30°$ more than the measure of the smallest angle. Therefore, this second acute angle can be represented as:
$x+30°$

According to the angle sum property of a triangle, the sum of all three interior angles in a triangle is always equal to $180°$. Setting up the equation:
$x+(x+30°)+90°=180°$

Now, let's simplify the equation step-by-step:
$2x+120°=180°$
Subtract $120°$ from both sides of the equation:
$2x=180°-120°$
$2x=60°$
Divide both sides by 2:
$x=30°$

Thus, the measure of the smallest angle is $30°$.