Question 502589

Let x and y be your two angles. Let y be the larger angle.


Because x and y are supplementary angles, we know that {{{x+y=180}}}


Since "One angle is twice its supplement increased by 21 degrees", this means that {{{y=2x+21}}}


{{{x+y=180}}}


{{{x+(2x+21)=180}}}


{{{x+2x+21=180}}}


{{{3x+21=180}}}


{{{3x=180-21}}}


{{{3x=159}}}


{{{x=159/3}}}


{{{x=53}}}


So the smaller angle is 53 degrees.


The larger angle is then {{{y=2x+21=2(53)+21=106+21=127}}} degrees.


So the two angles are 53 degrees and 127 degrees