Question 728546


Complementary angles add up to {{{90}}}°, and supplementary angles add up to {{{180}}}°

{{{alpha+beta=90}}}...=>..{{{alpha=90-beta}}}

let angles be {{{alpha}}} and {{{beta}}}; {{{beta}}} is complement to {{{alpha}}} and vs

if angle ({{{alpha}}}) whose supplement is seven times its complement {{{beta}}}

than we have

{{{alpha+7*beta=180}}}...substitute {{{alpha=90-beta}}}

{{{90-beta+7*beta=180}}}...solve for {{{beta}}}

{{{6*beta=180-90}}}

{{{6*beta=90}}}

{{{beta=90/6}}}

{{{highlight(beta=15)}}}

now find {{{alpha}}}

{{{alpha=90-15}}}

{{{highlight(alpha=75)}}}