竞赛第7题5分
若兩個鋭角的度數比是$$5$$ ：$$4$$，其中一個角的餘角是另一個角的餘角之$$2$$倍，則此兩角的度數和為何？  The ratio of the neasures of two acute angles is $$5:4$$, and the complement of one of these two angles is twice as  large as the complement of the other. What is the sun of the degree measures of the two angles?
We can set up a system of equations where $$x$$ and $$y$$ are the two acute angles. WLOG, assume that $$x\textless y$$ in order for the complement of $$x$$ to be greater than the complement of $$y$$.  Therefore, $$5x=4y$$ and $$\begin{array}{l} {90-x=2\left( 90-y\right)}  {90-x=2\left( 90-1.25x\right)}  {1.5x=90}  {x=60} \end{array}$$ Solving for $$y$$ in the first equation and substituting into the second equation yields Substituting this $$x$$ value back into the first equation yields $$y=75$$, leaving $$x+y$$ equal to $$\left(\text{C}\right) 135$$. 