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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.
