Question 316144
Lets call the two angles {{{x}}} and {{{y}}}. One of them is 15 + half of the other one. Written as an equation, this says {{{x = 15 + y/2 }}} (eq1). 

Since they are complimentary, we know that the angles add up to 90 degrees. Thus {{{x + y = 90}}}. We can rewrite this as {{{x = 90 - y}}} (eq2). 

Now (eq2) gives us an equation for {{{x}}} that we can substitute into (eq1). 

{{{x = 90 -  y = 15 + y/2}}}. 

{{{ 90 - y = 15 + y/2 }}} 

Add y to both sides to get 

{{{ 90 = 15 + 3y/2 }}} 

Subtract 15 from both sides to get 

{{{ 75 = 3y/2 }}} 

Multiply both sides by 2 to get 

{{{ 150 = 3 y}}} 

Divide both sides by 3 to get 

{{{ 50  = y }}} 

Thus, from (eq2), we know that {{{x=90-y=90-50=40}}} 

Now we check: 40 and 50 do add up to 90, so they are complimentary. 

Also, one of them is 15 plus half of the other since 

15 + half of 50 = 15 + 25 = 40