Question 1046461
if an acute angle  is {{{A}}}, then

the complement of an acute angle {{{A}}} is the angle {{{90-A}}}°

the  supplement of an acute angle {{{A}}} is the angle {{{180-A}}}°

given:
The measure of the supplement of an angle is {{{30}}}° less than {{{five}}} {{{ times}}} the measure of the complement; so, we have

{{{(180-A)+30=5(90- A)}}}°

{{{210-A=450-5A}}}°

{{{5A -A=450 -210}}}°

{{{4A=240}}}°

{{{A=240/4}}}°

{{{highlight(A=60)}}}°


the complement of an acute angle {{{A}}} is the angle {{{90-60=highlight(30)}}}°


and two-fifths the measure of the complement is {{{(2/5)30=(2/cross(5)1)cross(30)6=2*6=highlight(12)}}}°