# Chapter 1 - Tools of Geometry - 1-5 Exploring Angle Pairs - Practice and Problem-Solving Exercises - Page 39: 37

a) x=19.5 b) $m\angle RQS=43$, $m\angle TQS=137$ c) $m\angle RQS+m\angle TQS\overset?=180$ $43+137\overset?=180$ $180=180\checkmark$

#### Work Step by Step

Use the definition of a linear pair: $m\angle RQS+m\angle TQS=180$ $(2x+4)+(6x+20)=180$ $8x+24=180$ $8x+24-24=180-24$ $8x=156$ $8x\div8=156\div8$ $x=19.5$ Substitute to find the measures: $m\angle RQS=2x+4+2(19.5)+4=39+4=43$ $m\angle TQS=6x+20=6(19.5)+20=117+20=137$ To check your answer, verify the sum of the angles is 180.

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