Answer
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.
