SOLUTION: ∠ RQS and ∠ TQS are vertical angles where m∠ RQS = 3(x + 7) and m∠ TQS = 4x + 15. Solve for x. Find m∠ RQS and m∠ TQS Show how you can

Algebra ->  Angles -> SOLUTION: ∠ RQS and ∠ TQS are vertical angles where m∠ RQS = 3(x + 7) and m∠ TQS = 4x + 15. Solve for x. Find m∠ RQS and m∠ TQS Show how you can      Log On


   

Question 788896: ∠ RQS and ∠ TQS are vertical angles where m∠ RQS = 3(x + 7) and m∠ TQS = 4x + 15.
Solve for x.
Find m∠ RQS and m∠ TQS
Show how you can check your answer.
Thank you for helping me! \(^-^)/
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
∠ RQS and ∠ TQS are vertical angles

so that means they are congruent (since vertical angles are congruent)

so set them equal, plug in the given expressions, then solve for x

m ∠ RQS = m ∠ TQS

3(x + 7) = 4x + 15

3x+21 = 4x+15

3x = 4x+15-21

3x-4x = 15-21

-x = 15-21

-x = -6

x = (-6)/(-1)

x = 6

-------------------------------------------------------

Since x = 6, we know that

m ∠ RQS = 3(x + 7)

m ∠ RQS = 3(6 + 7)

m ∠ RQS = 3(13)

m ∠ RQS = 39 degrees

Angle TQS is also 39 degrees (since the two angles are congruent vertical angles). I'll let you determine angle TQS (plug x = 6 into the second equation and evaluate).