Question 1183871

let the two acute angels be {{{alpha}}} and {{{beta}}}

if they  are in the ratio {{{1:4}}}, we have

{{{alpha:beta=1:4}}}........solve for {{{beta}}}

{{{beta=4alpha}}}.........eq.1

if {{{alpha}}} and {{{beta}}} are two acute angels of a right triangle, their sum is {{{90}}}°  

{{{alpha + beta=90}}}.........eq.2

substitute {{{beta}}} from eq.1

{{{alpha+4alpha=90}}}

{{{5alpha=90}}}

{{{alpha=90/5}}}

{{{highlight(alpha=18)}}}°

then

{{{beta=4*18}}}

{{{highlight(beta=72)}}}°