SOLUTION: The measure of angle K is 16 degrees less than 3 times the measure of its supplement. Find the measure of angle K

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Question 147562: The measure of angle K is 16 degrees less than 3 times the measure of its supplement. Find the measure of angle K
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2By=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%2By=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%2B16Add 16 to both sides


4y=196 Combine like terms on the right side


y=%28196%29%2F%284%29 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%2849%29-16 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.