Answer
x = 20
m$\angle$RSV = 56$^{\circ}$
Work Step by Step
Using the Segment Addition Postulate:
m$\angle$RST + m$\angle$TSV = m$\angle$RSV
Substitute in the values from the problem.
(2x - 10) + (x + 6) = 4(x - 6)
Simplify.
3x -4 = 4x - 24
Subtract 3x from both sides.
3x - 3x - 4 = 4x - 3x - 24
-4 = x - 24
Add 24 to both sides.
-4 + 24 = x - 24 + 24
20 = x
Substitute the value of 20 into the measurement of $\angle$RSV
m$\angle$RSV = 4(x - 6)
m$\angle$RSV = 4(20 - 6)
m$\angle$RSV = 56$^{\circ}$
