1. The problem asks to find the measure of the given acute angle in degrees using a protractor. 2. The angle is formed by one ray extending horizontally to the right and the other ray extending up-right from the same vertex. 3. Since the angle is acute, its measure is between 0 and 90 degrees. 4. Using a protractor, align the baseline with the horizontal ray and read the scale where the up-right ray crosses. 5. The angle measure is approximately 45 degrees. 6. Therefore, the measure of the angle is $45^\circ$.