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)   (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 . Also, since "measure of angle K is 16 degrees less than 3 times the measure of its supplement", this tells us that


Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.


Combine like terms on the left side


Add 16 to both sides


Combine like terms on the right side


Divide both sides by 4 to isolate y



Divide




Now that we know that , we can plug this into to find



Substitute for each


Simplify


So our answer is and . So the measure of angle K is 131 degrees.
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