Question 958599

two angles ({{{alpha}}}° and {{{beta}}}°) are Complementary Angles if they add up to {{{90}}}°

so, {{{alpha+beta=90}}}°

given: one of two complementary angles (let's say {{{alpha}}}) measures {{{30}}}° {{{ more}}} than {{{three}}}{{{ times}}} the other (let's say {{{beta}}}°)

so, we have that {{{alpha=3beta+30}}}° => substitute it in {{{alpha+beta=90}}}°

{{{3beta+30+beta=90}}}°........solve for {{{beta}}}

{{{4beta=90-30}}}°

{{{4beta=60}}}°

{{{beta=60/4}}}°

{{{highlight(beta=15)}}}°

now find {{{alpha}}}

{{{alpha=3beta+30}}}°

{{{alpha=3*15+30}}}°

{{{alpha=45+30}}}°

{{{highlight(alpha=75)}}}°