Question 1152344
let angles be {{{alpha}}} and {{{beta}}}

if angle {{{alpha}}} is {{{27}}} less than {{{2}}} times {{{beta}}}, we have

{{{alpha=2beta-27}}}........eq.1

 
a.They are complements of each other.
 
complementary angles are two angles whose sum is {{{90}}}° 

=>{{{alpha+beta=90}}}....substitute {{{alpha}}} from eq.1

{{{2beta-27+beta=90}}}

{{{3beta=90+27}}}

{{{3beta=117}}}

{{{beta=117/3}}}

{{{beta=39}}}° 


then,

{{{alpha=2beta-27}}}........eq.1

{{{alpha=2*39-27}}}

{{{alpha=51}}}° 


b.They are supplements of each other.

supplementary angles are two angles whose sum is {{{180}}}° 

=>{{{alpha+beta=180}}}....substitute {{{alpha}}} from eq.1

{{{2beta-27+beta=180}}}

{{{3beta=180+27}}}

{{{3beta=207}}}

{{{beta=207/3}}}

{{{beta=69}}}°

then,

{{{alpha=2beta-27}}}........eq.1

{{{alpha=2*69-27}}}

{{{alpha=111}}}° 


so, 
complementary angles are: {{{ 51}}}° and {{{39}}}° 

supplementary angles are: {{{ 111}}}° and {{{69}}}°