SOLUTION: Please,please, help me I am having a horrible time with this class. angle PQR, and angle ABC are supplementary, and angle PQR is three times as large as angle ABC. Determine th

Algebra ->  Angles -> SOLUTION: Please,please, help me I am having a horrible time with this class. angle PQR, and angle ABC are supplementary, and angle PQR is three times as large as angle ABC. Determine th      Log On


   

Question 478947: Please,please, help me I am having a horrible time with this class.
angle PQR, and angle ABC are supplementary, and angle PQR is three times as large as angle ABC. Determine the measure of each angle, show work step by step.
Found 2 solutions by MathLover1, Earlsdon:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

angle PQR, and angle ABC are supplementary, ...Supplementary angles are pairs of angles that add up to 180+
so, PQR+%2B+ABC=180.........1

and angle PQR is three times as large as angle ABC:
PQR=3ABC....2...substitute in 1

Determine the measure of each angle:
PQR=3ABC....2...substitute in 1
3ABC+%2B+ABC=180.........1
4ABC=180
ABC=180%2F4

ABC=45....now find PQR
PQR=3ABC....2
PQR=3%2A45
PQR=135





Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Two angles are supplementary when their sum is 180 degrees, so...
1) PQR%2BABC+=+180
The problem states that:
2) PQR+=+3%28ABC%29 Substitute this into equation 1) for angle PQR.
1a) 3%28ABC%29%2BABC+=+180 Simplify.
1b) 4%28ABC%29+=+180 Divide both sides by 4.
1c) highlight%28ABC+=+45%29%29degrees and...
PQR+=+3%28ABC%29
PQR+=+3%2845%29
highlight%28PQR+=+135%29degrees.