Question 647714

supplementary angles, because they add up to {{{180}}}°

so, {{{alpha+beta=180}}}....1

so, {{{alpha-beta}}}....the difference

given: the sum of two supplementary angles {{{exceeds}}} the difference of their measures by {{{116}}} degrees.

{{{alpha+beta=alpha-beta+116}}}....2...solve for {{{beta}}}

{{{cross(alpha)+beta=cross(alpha)-beta+116}}}

{{{beta=-beta+116}}}

{{{beta+beta=116}}}

{{{2*beta=116}}}

{{{beta=116/2}}}

{{{beta=58}}}

now find {{{alpha}}}

{{{alpha+beta=180}}}....1

{{{alpha=180-beta}}}

{{{alpha=180-58}}}

{{{alpha=122}}}