You have an isosceles triangle, a hemi-circle and another circle [in the top].

Try writing down as many variables as possible with your picture and show us the work you have done to write them as formulas so we can give you a hand.

Well, inside the triangle I have 2alpha + beta = 180deg.
Using the Angle in the Center Theorem I get a X that is two times bigger than my beta (beta = x/2)
Implementing that in 2alpha + beta = 180deg i came with the result that alpha is equal to 90deg - x/4.
That's all i can get from the information given.

Thanks, this helped a lot. Now i just express \(\displaystyle \beta \) from the first triangle, which is \(\displaystyle 180{}^{\circ} - 2 \alpha \) , put in the \(\displaystyle \alpha +3\beta =180{}^{\circ}\) and i get that \(\displaystyle \alpha = 360{}^{\circ} /5 \) which is \(\displaystyle 72{}^{\circ} \) and the right answer. Thanks!