Question 98610
Let x=angle 1, y=angle 2


Since one angle (say angle 2) is 21 more (ie add 21) than twice (2 times) the other angle, we get


{{{y=2x+21}}}



Now add the angles x and y to get 90 degrees (remember two complementary angles add up to 90 degrees)


{{{x+y=90}}}


{{{x+2x+21=90}}} Plug in {{{y=2x+21}}}






{{{3x=90-21}}}Subtract 21 from both sides



{{{3x=69}}} Combine like terms on the right side



{{{x=(69)/(3)}}} Divide both sides by 3 to isolate x




{{{x=23}}} Divide


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Answer:

So our angle is {{{x=23}}}



{{{y=2(23)+21}}} Now plug in  {{{x=23}}} to find y


{{{y=46+21}}} Multiply


{{{y=67}}} Add



So the other angle is {{{y=67}}}



So the two angles are 23 and 67 degrees


Check:



{{{23+67=90}}} Add up the angles, the left side should add up to the right side


{{{90=90}}} Since the equation is true, our answer is verified