Question 777253
1) If two angles are supplementary, the sum of their measures is 180 deg.
Let measure of ABC be x. Then measure of DEF = 3*x - 20 (i.e. 20 less than
3 times the measure of ABC)
Since their sum is 180, we have the equation
{{{x + 3*x - 20 = 180}}}
{{{4*x = 200}}}
{{{x = 50}}}
So ABC is 50 deg and DEF = 130 deg.

2) Since SQ bisects RST, 
RSQ = QST = RST/2 
QST = 2*x + 18, RST = 6*x - 2
QST = RST/2
i.e {{{2*x + 18 = (6*x - 2)/2 = 3*x - 1}}}
Subtracting 2x from both sides
{{{18 = 3*x - 2*x - 1 = x - 1}}}
{{{x = 19}}}
So QST = 2*x + 18 = 2*19 + 18 = 56 deg
RSQ is also equal to 56 deg.
Check for correctness: RST = 6*x - 2 = 6*19 - 2 = 112 deg, which is twice the
measure of RSQ and QST which is 56 deg. So it is the correct solution.
Hope you got it :)