Question 907635



let's angles be {{{alpha}}} and its supplement {{{beta}}}


supplementary angles - two angles that add to {{{180}}} degrees:

so,  we have  {{{alpha+beta=180}}} .eq.1.....

if the measure of {{{alpha}}} is one third the measure of its supplement {{{beta}}}, than we have {{{alpha= (1/3)beta}}} ....eq.2

start with 

{{{alpha+beta=180}}} ...eq.1.....substitute {{{alpha}}} from eq.2

{{{(1/3)beta+beta=180}}}

{{{ 3(1/3)beta+3beta=180*3}}}

{{{ beta+3beta=540}}}

{{{ 4beta=540}}}

{{{ beta=540/4}}}

{{{ beta=135}}}

now find {{{alpha}}}

{{{alpha= (1/3)beta}}} ....eq.2

{{{alpha= (1/3)135}}} 

{{{alpha= 45}}}