Question 106102
Let's call the angles A and B. 
1. {{{A+B=90}}}
2. {{{A/B=4/11}}}
Use equation 2 to solve for A in terms of B and substitute back into equation 1.
2. {{{A/B=4/11}}}
{{{A=B*(4/11)}}}
Now into equation 1. 
1. {{{A+B=90}}}
{{{B*(4/11)+B=90}}}
{{{B*(4/11)+B*(11/11)=90}}}
{{{B*(15/11)=90}}}
{{{B=90*(11/15)}}}
{{{B=66}}}
{{{A=B*(4/11)=66*(4/11)=24}}}
Check your answers.
1. {{{A+B=90}}}
{{{24+66=90}}}
{{{90=90}}}
Good answer.
2. {{{A/B=4/11}}}
{{{24/66=4/11}}}
{{{(6/6)*(4/11)=4/11}}}
{{{4/11=4/11}}}
Good answer.
Your angles are {{{24^o}}} and {{{66^o}}}