Final answer:
After solving the equations for angles α and β of a right triangle, it is determined that angle α is approximately 49°, which is not listed in the multiple-choice options provided.
Step-by-step explanation:
To solve for angle α in a right triangle, where angles α and β are acute and given by the expressions α = 5x-20 and β = 2x+14, we make use of the fact that the sum of the angles in a triangle equals 180°. Since we have a right triangle, we know that α + β + 90° = 180°, which gives us the equation α + β = 90°. Substituting the given expressions, we get 5x-20 + 2x+14 = 90.
Solving this equation for x, we have 7x - 6 = 90, so x = 96/7, which simplifies to approximately 13.71. Now, we substitute x back into the expression for α, obtaining α = 5(13.71) - 20. Doing the math, α = 68.55 - 20, which equals 48.55°. Rounded to the nearest degree, α is approximately 49°.
None of the options 24°, 30°, 60°, or 66° match the calculated value of α; therefore, it seems there may have been an error in the options provided or in the interpretation of the expressions representing the angles. The correct value is approximately 49°.