Question 147562
Let x=measure of angle K and y=measure of supplement to angle K


Supplemental angles add to 180 degrees. So this means that {{{x+y=180}}}. Also, since "measure of angle K is 16 degrees less than 3 times the measure of its supplement", this tells us that {{{x=3y-16}}}



{{{3y-16+y=180}}}  Plug in {{{x=3y-16}}} into the first equation. In other words, replace each {{{x}}} with {{{3y-16}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{4y-16=180}}} Combine like terms on the left side



{{{4y=180+16}}}Add 16 to both sides



{{{4y=196}}} Combine like terms on the right side



{{{y=(196)/(4)}}} Divide both sides by 4 to isolate y




{{{y=49}}} Divide





Now that we know that {{{y=49}}}, we can plug this into {{{x=3y-16}}} to find {{{x}}}




{{{x=3(49)-16}}} Substitute {{{49}}} for each {{{y}}}



{{{x=131}}} Simplify



So our answer is {{{x=131}}} and {{{y=49}}}. So the measure of angle K is 131 degrees.