Question 1126292

Supplementary angles are two angles that have a sum of {{{180}}}°.

Complementary angles are two angles that have a sum of {{{90}}}°.

i angle is {{{alpha}}}, its supplement is {{{180- alpha}}}, and its complement is {{{90- alpha}}}

if the sum of the measures of a complement and a supplement of an angle is {{{160}}}, we have

{{{(180- alpha)+(90- alpha)=160}}}...solve or {{{alpha}}}

{{{180- alpha+90- alpha=160}}}

{{{270- 2alpha=160}}}

{{{270-160 = 2alpha}}}

{{{110 = 2alpha}}}

{{{alpha=110 /2}}}

{{{alpha=55}}}°

check:

if {{{alpha=55}}}, its supplement is {{{180- alpha=180-55=125}}}
if {{{alpha=55}}}, its complement is {{{90- alpha=90-55=35}}}

{{{125+35=160}}}
{{{160=160}}}