Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 1 - Section 1.4 - Angles and Their Relationships - Exercises: 19

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$^{\circ}$
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