Question 921725

given:

An angle {{{alpha}}}  is  {{{45}}}  degree less  than  two  times  of its supplement {{{beta}}}:

{{{alpha=2beta-45}}}.......eq.1
 
Two angles are called supplementary angles if the sum of their degree measurements equals {{{180}}] degrees.

 than  the greater  angle  is

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

{{{2beta-45+beta=180}}}

{{{3beta=180+45}}}

{{{3beta=225}}}

{{{beta=225/3}}}

{{{beta=75}}}

and {{{alpha=180-beta}}}=>{{{alpha=180-75}}}=>{{{alpha=105}}}

so, the greater  angle  is {{{alpha=105}}}