SOLUTION: Given: m∠RST = (2x − 10)° m∠TSV = (x + 7)° m∠RSV = (4(x − 7))° Find: x and m∠RSV in degree

Algebra ->  Angles -> SOLUTION: Given: m∠RST = (2x − 10)° m∠TSV = (x + 7)° m∠RSV = (4(x − 7))° Find: x and m∠RSV in degree      Log On


   

Question 1191249: Given:
m∠RST = (2x − 10)°
m∠TSV = (x + 7)°
m∠RSV = (4(x − 7))°
Find: x and m∠RSV in degree
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
m∠RST = (2x − 10)°
m∠TSV = (x + 7)°
m∠RSV = (4(x − 7))°
Find: x and m∠RSV in degree
------------------------
How are the angles related?
What shape is RSTV?

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is obvious that  ∠RST   + ∠TSV  = ∠RSV.


Hence,             (2x-10) + (x+7) = 4(x-7).


Simplify and find x

    2x - 10 + x + 7 = 4x - 28,

        3x  - 3     = 4x - 28,

        28  - 3     = 4x - 3x,

           25       = x.


Thus  x= 25 degrees  and  m∠RSV = 4(25 − 7) = 72 degrees.     ANSWER

Solved.