Question 147554
Complementary angles add up to 90 degrees. So let x be the complement to angle y. Since "The measure of angle Y is twice the measure of its complement", this means that {{{y=2x}}}. Also, since the two angles add up to 90, this means that {{{x+y=90}}}  



{{{x+(2x)=90}}}  Plug in {{{y=2x}}} into the second equation. In other words, replace each {{{y}}} with {{{2x}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{3x=90}}} Combine like terms on the left side



{{{x=(90)/(3)}}} Divide both sides by 3 to isolate x




{{{x=30}}} Divide





Now that we know that {{{x=30}}}, we can plug this into {{{y=2x}}} to find {{{y}}}




{{{y=2(30)}}} Substitute {{{30}}} for each {{{x}}}



{{{y=60}}} Simplify



So our answer is {{{x=30}}} and {{{y=60}}}. So the measure of the complement of angle y is 30 degrees.