SOLUTION: I have been working on this problem for awhile now and I still can't figure it out. I was wondering if someone would help me? Please and Thank You!! I would deeply appreciate it!!

Algebra ->  Angles -> SOLUTION: I have been working on this problem for awhile now and I still can't figure it out. I was wondering if someone would help me? Please and Thank You!! I would deeply appreciate it!!       Log On


   

Question 154571This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this problem for awhile now and I still can't figure it out. I was wondering if someone would help me? Please and Thank You!! I would deeply appreciate it!!
The measure of the supplement of an angle is 12 degress greater than three times the measure of a complement. Find the measure of the angle. This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=measure of original angle, y=measure of the supplementary angle and z=measure of the complementary angle

Remember supplemental angles add to 180 degrees and complementary angles add to 90 degrees. So this means that x%2By=180 and x%2Bz=90


x%2By=180 Start with the first equation.


y=180-x Subtract "x" from both sides.


x%2Bz=90 Move onto the second equation.


z=90-x Subtract "x" from both sides.



Since "measure of the supplement of an angle is 12 degrees greater than three times the measure of a complement" this means that the third equation is y=3z%2B12


y=3z%2B12 Start with the third equation.


180-x=3%2890-x%29%2B12 Plug in y=180-x and z=90-x


180-x=270-3x%2B12 Distribute.


180-x=-3x%2B282 Combine like terms on the right side.


-x=-3x%2B282-180 Subtract 180 from both sides.


-x%2B3x=282-180 Add 3x to both sides.


2x=282-180 Combine like terms on the left side.


2x=102 Combine like terms on the right side.


x=%28102%29%2F%282%29 Divide both sides by 2 to isolate x.


x=51 Reduce.


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Answer:

So the answer is x=51 which means that the angle is 51 degrees