Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 1 - Tools of Geometry - 1-4 Measuring Angles - Practice and Problem-Solving Exercises: 23

Answer

m$\angle$RQS = 43$^{\circ}$ m$\angle$TQS = 137$^{\circ}$

Work Step by Step

$\angle$RQS and $\angle$TQS are supplementary angles, meaning they equal 180$^{\circ}$ when added together. To solve, add the two equations together, set them equal to 180, and then solve for the variable: (6x + 20) + (2x + 4) = 180$^{\circ}$ 8x + 24 = 180$^{\circ}$ 8x = 156$^{\circ}$ x = 19.5$^{\circ}$ Now, plug this x value back into the original equations: m$\angle$RQS = 2x +4 = 2(19.5) + 4 = 39 + 4 = 43$^{\circ}$ m$\angle$TQS = 6x + 20 = 6(19.5) + 20 = 117 + 20 = 137$^{\circ}$
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