SOLUTION: I need help please 1) angle ABC and angle DEF are supplementary angles. The measure of angle DEF is twenty degrees less than three times the measure of angle ABC. What are the me

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Question 777253: I need help please
1) angle ABC and angle DEF are supplementary angles. The measure of angle DEF is twenty degrees less than three times the measure of angle ABC. What are the measures m angle ABC and m angle DEF?
2) line SQ bisects angle RST . m angle QST = 2x+18 and m angle RST =6x-2. What is m angle RSQ?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
1) If two angles are supplementary, the sum of their measures is 180 deg.
Let measure of ABC be x. Then measure of DEF = 3*x - 20 (i.e. 20 less than
3 times the measure of ABC)
Since their sum is 180, we have the equation
x+%2B+3%2Ax+-+20+=+180
4%2Ax+=+200
x+=+50
So ABC is 50 deg and DEF = 130 deg.
2) Since SQ bisects RST,
RSQ = QST = RST/2
QST = 2*x + 18, RST = 6*x - 2
QST = RST/2
i.e 2%2Ax+%2B+18+=+%286%2Ax+-+2%29%2F2+=+3%2Ax+-+1
Subtracting 2x from both sides
18+=+3%2Ax+-+2%2Ax+-+1+=+x+-+1
x+=+19
So QST = 2*x + 18 = 2*19 + 18 = 56 deg
RSQ is also equal to 56 deg.
Check for correctness: RST = 6*x - 2 = 6*19 - 2 = 112 deg, which is twice the
measure of RSQ and QST which is 56 deg. So it is the correct solution.
Hope you got it :)