Question 173134
let x=first non-right angle and y=second non-right angle


The "non-right angles in a right triangle" are complementary. This means that they add to 90 degrees.



So this means that {{{x+y=90}}}



Now since "twice the first is 16 more than twice the second", this tells us that {{{2x=2y+16}}}



{{{2x=2y+16}}} Start with the second equation



{{{x=(2y+16)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=(2y)/(2)+(16)/(2)}}} Break up the fraction



{{{x=y+8}}} Reduce



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{{{x+y=90}}} Go back to the first equation



{{{y+8+y=90}}} Plug in {{{x=y+8}}}



{{{2y+8=90}}} Combine like terms on the left side.



{{{2y=90-8}}} Subtract {{{8}}} from both sides.



{{{2y=82}}} Combine like terms on the right side.



{{{y=(82)/(2)}}} Divide both sides by {{{2}}} to isolate {{{y}}}.



{{{y=41}}} Reduce. So the second angle is 41 degrees



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{{{x=y+8}}} Go back to the previously isolated equation



{{{x=41+8}}} Plug in {{{y=41}}}



{{{x=49}}} Add. So the first angle is 49 degrees



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Answer:



So the solutions are {{{x=49}}} and {{{y=41}}} which means that the first non-right angle is 49 degrees and the second non-right angle is 41 degrees