Question 212281
Let S = measure of supplement


So by definition {{{S+T=180}}} (since supplemental angles add to 180 degrees). Also, since "the measure of angle T is 20 more than four times its supplement", this means {{{T=4S+20}}}



{{{S+T=180}}} Start with the first equation.



{{{S+4S+20=180}}} Plug in {{{T=4S+20}}}



{{{20+5S=180}}} Combine like terms on the left side.



{{{5S=180-20}}} Subtract {{{20}}} from both sides.



{{{5S=160}}} Combine like terms on the right side.



{{{S=(160)/(5)}}} Divide both sides by {{{5}}} to isolate {{{s}}}.



{{{S=32}}} Reduce.



----------------------------------------------------------------------


Answer:


So the solution is {{{S=32}}} 



This means that the supplemental angle is 32 degrees while angle T is {{{T=4(32)+20=128+20=148}}} degrees.