Me angles α and β are the two acute angles in a right triangle, where α = 5x/3 + 20 and β = 2x/3+ 14. find α. a) 24° b) 30° c) 60° d) 66°

Short Answer C
Nice little problem. The catch is that alpha and beta both add up to 90 degrees. 
Here's why.

α + β + right angle = 180° All triangles have 180° A right and = 90°.
α + β + 90 = 180  Right angles are 90° Now subtract 90° from both sides
α + β = 180 - 90
α + β = 90

Now all you have to do is put in the x values for alpha and beta and equate them to 90

5x/3 + 20 + 2x/3 + 14 = 90  Collect the light terms.
5x/3 + 2x/3 + 20 + 14 = 90
7x/3 + 34 = 90                     Subtract 24 from both sides.
7x/3 = 90 - 34                           
7x/3 = 56                             Multiply by sides by 3
7x = 3*56
7x = 168                              Divide by 7
x = 168/7
x = 24

That's not quite the answer
The question wants alpha.
α = 5x / 3 + 20
α = 5*24/3 + 20
α = 120/3 + 20
α = 40 + 20
α = 60

Answer C <<<<<<