SOLUTION: Given ST bisects angle RSV m of angle RST =2x+3y m of angle TSV = 3x-y+2 m of angle RSV = 80 degrees Find x and y. I am not sure how y and x separate

Algebra ->  Angles -> SOLUTION: Given ST bisects angle RSV m of angle RST =2x+3y m of angle TSV = 3x-y+2 m of angle RSV = 80 degrees Find x and y. I am not sure how y and x separate      Log On


   

Question 939781: Given ST bisects angle RSV
m of angle RST =2x+3y
m of angle TSV = 3x-y+2
m of angle RSV = 80 degrees
Find x and y.
I am not sure how y and x separate ? please help! can you show me how to do this?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


if ST bisects angle RSV means divides angle into two equal parts, angle RST and angle TSV
it means m <RSV=m <RST+m <TSV
if m < RST+=2x%2B3y
m < TSV+=+3x-y%2B2

m < RSV+=+80 degrees
and if m <RSV=m <RST+m <TSV, then
m < 2x%2B3y=40........eq.1
m < +3x-y%2B2=40......eq.2
-----------------------------------------------
solve the system:
2x%2B3y=40........eq.1
+3x-y%2B2=40......eq.2....both sides multiply by 3
-----------------------
2x%2B3y=40........eq.1
+9x-3y%2B6=120......eq.2.
------------------------------------add
2x%2Bcross%283y%29%2B9x-cross%283y%29%2B6=40%2B120
2x%2B9x%2B6=160
11x=160-6
11x=154
x=154%2F11
x=14

go to +3x-y%2B2=40......eq.2 substitute 14 for x and solve for y
+3%2A14-y%2B2=40
+42-y%2B2=40
+44-40=y
+4=y
so, the m <RST and m <TSV is:

m < RST+=2x%2B3y=>m < RST+=2%2A14%2B3%2A4m < RST+=28%2B12=>m < RST+=40
m < TSV+=+3x-y%2B2=>m < TSV+=+3%2A14-4%2B2=>m < TSV+=+42-4%2B2=>m < TSV+=+44-4=>m < TSV+=40