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.Com
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)   (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).

RELATED QUESTIONS

∠ 1 and ∠ 2 are complementary angles. ∠ 1 and ∠ 3 are vertical... (answered by macston)
∠A and ∠B are vertical angles. If m∠A=(2x+15)∘ and... (answered by Boreal,ikleyn,Alan3354)
∠E and ∠F are vertical angles with m ∠E=9x+12 and m ∠F=3x+24... (answered by jim_thompson5910)
∠A and ​ ∠B ​ are vertical angles with m∠A=x and... (answered by math_helper)
∠A and ∠B are vertical angles. If m∠A=(x+25)∘ and... (answered by stanbon)
∠A and ∠B are vertical angles. m∠A = 125° and m∠B = (x - 10)°.... (answered by fractalier)
Triangle ABC has an exterior angle, ∠DAB, and two remote inner angles, ∠B and (answered by ankor@dixie-net.com)
∠A and ∠B\angle B∠B are vertical angles. If... (answered by josgarithmetic)
if ∠a and ∠b are complementary angles and m∠a=5m∠b, find... (answered by Edwin McCravy)