Let's label the vertices clockwise starting with the topmost vertex. Let's call them $\displaystyle A,B,C,D,E$. Let's call the vertex in the center $\displaystyle F$. Triangle ABE is similar to triangle CDF. You will want to show that BF=FE=1 and FC=FD=(x-1). Then $\displaystyle \dfrac{1}{x-1} = \dfrac{EA}{FD} = \dfrac{BE}{CD} = \dfrac{x}{1}$.