Final answer:
The measure of each angle of the dilated figure is 90 degrees, 30 degrees, and 60 degrees.
Step-by-step explanation:
To find the measure of each angle of the dilated figure, we first need to determine the measure of the angles in the original right triangle. We know that one angle is 90 degrees and another angle is 30 degrees. To find the third angle, we use the fact that the sum of the angles in a triangle is 180 degrees. So, the third angle is 180 - 90 - 30 = 60 degrees.
Since the triangle is dilated by a scale factor of 3, all the angles in the dilated figure will remain the same. Therefore, each angle of the dilated figure will measure 90 degrees, 30 degrees, and 60 degrees.