Question 1188611

Two angles are called complementary when their measures add to {{{90}}}°. 

let the larger angle be {{{alpha}}} and the smaller angle {{{beta}}}


{{{alpha+beta=90}}} ..........eq.1


 if the larger angle exceeds {{{three}}} times the smaller by {{{38}}}°, we have 


{{{alpha=3beta+38}}} .........eq.2


substitute {{{alpha}}} in eq.1


{{{3beta+38+beta=90}}} ..........eq.1, solve for {{{beta}}}

{{{4beta=90-38}}}

{{{4beta=52}}}

{{{beta=13}}}°


go to

{{{alpha=3beta+38}}} .........eq.2, substitute {{{beta}}}

{{{alpha=3*13+38}}} 

{{{alpha=77}}}°