## Elementary Geometry for College Students (5th Edition)

x = 20 m$\angle$RSV = 56$^{\circ}$
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$^{\circ}$