SOLUTION: I have to figure out the measure of the angles. The problem is "find the measure of angle T if the measure of angle T is 20 more than four times its supplement" I know the answer i

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Question 212281: I have to figure out the measure of the angles. The problem is "find the measure of angle T if the measure of angle T is 20 more than four times its supplement" I know the answer is 148 but I can't figure out how to get to that. I tried solving it by setting up the equation 4t+20=180 but I got 40. And I just really can't figure out how to so this. Please help!!
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Let S = measure of supplement

So by definition S%2BT=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%2B20


S%2BT=180 Start with the first equation.


S%2B4S%2B20=180 Plug in T=4S%2B20


20%2B5S=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=%28160%29%2F%285%29 Divide both sides by 5 to isolate s.


S=32 Reduce.


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Answer:

So the solution is S=32


This means that the supplemental angle is 32 degrees while angle T is T=4%2832%29%2B20=128%2B20=148 degrees.