In a right triangle, the acute angles measure x + 15 and 2x degrees. What is the measure of the smallest angle of the triangle?

The sum of the three angles of a triangle is always 180 degrees. If the triangle is right, which means one of the angles measures 90 degrees, the other two angles should add up to 90 degrees. With this condition and the given above, x + 15 + 2x = 90. Solving for x in the equation gives x = 25. Substituting x to the given expression for the acute angles gives the measurements of 40 and 50 degrees. Thus, the smallest angle of the triangle is 40 degrees.