Question 161930
Complementary angles ALWAYS add to 90 degrees. So this means that {{{x+y=90}}}. Since "difference between two complementary angles is 50 degrees", this means that {{{x-y=50}}}



So we have the system of equations:

{{{system(x+y=90,x-y=50)}}}



Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(x+y)+(x-y)=(90)+(50)}}}



{{{(x+x)+(y-y)=90+50}}} Group like terms.



{{{2x+0y=140}}} Combine like terms. Notice how the y terms cancel out.



{{{2x=140}}} Simplify.



{{{x=(140)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=70}}} Reduce. So the first angle is 70 degrees.



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{{{x+y=90}}} Now go back to the first equation.



{{{70+y=90}}} Plug in {{{x=70}}}.



{{{70+y=90}}} Multiply.



{{{y=90-70}}} Subtract {{{70}}} from both sides.



{{{y=20}}} Combine like terms on the right side. So the second angle is 20 degrees



So our answer is {{{x=70}}} and {{{y=20}}}. So the larger angle is 70 degrees.