Question 547713
Let's recall what complementary angles really are:
Two angles are complement if they sum to 90 degrees.  

Okay, so for the first question we will let x be the angle so the other angle must be x-60.  Since they are each others complement we know:
{{{(x-60)+x=90}}}
{{{2x-60=90}}}
{{{2x-60+60=90+60}}}
{{{2x=150}}}
{{{2x/2=150/2}}}
{{{x=75}}}
So the two angles are 75 and 75-60=15.
This means that the ratio between the two is 75:15  which can be reduced to 5:1.  



For the second question, it is very similar...
Let y be the angle so then the other angle is y-30.
{{{y+(y-30)=90}}}
{{{2y-30=90}}}
{{{2y=120}}}
{{{y=60}}}
So the two angles are 60 and 60-30=30.   
This means that the ratio of the smaller to the larger angle is 30:60 which can be reduced to 1:2.