Question 1124436


recall:

Two angles are complementary when they add up to {{{90}}} degrees (a right angle).


Two angles are supplementary when they add up to {{{180}}} degrees.

given:

the measure of angle {{{a= x-8}}}, and 
measure of angle {{{b= 3 (x+2/3)}}}

{{{x-8+ 3 (x+2/3)=90}}}

{{{x-8+ 3x+cross(3)(2/cross(3))=90}}}

{{{x-8+ 3x+2=90}}}

{{{4x-6=90}}}

{{{4x=90+6}}}

{{{4x=96}}}

{{{x=96/4}}}

{{{highlight(x=24)}}}

then

{{{a= x-8}}}->{{{a= 24-8}}}->{{{highlight(a=16)}}}

{{{b= 3 (x+2/3)}}}->{{{b= 3 (24+2/3)}}}->{{{b= 72+3(2/3)}}}->{{{b= 72+2}}}->{{{highlight(b= 74)}}}

then,  the supplement of angle {{{b}}} will be {{{180-b=180-74=highlight(106)}}}