Question 1154687

given:

 {{{DE}}} and {{{BC}}} are parallel, 

 < {{{3}}} = < {{{4}}} = {{{2}}}*< {{{2}}} 

 from the graph we see that

<{{{ 1}}}= < {{{5}}} + <{{{6 }}}  as corresponding angles  

< {{{5}}} = < {{{2}}}  as alternate interior angles


if < {{{3}}} = < {{{4}}} = {{{2}}}*< {{{2}}}, < {{{5}}} = < {{{2}}} , and if < {{{2}}} is {{{x}}} 

their sum is 
  
{{{2x+ 2x+ x=180}}
{{{5x=180}}
{{{x=36}}°=>  {{{m}}} < {{{2}}}={{{36}}}° and {{{m}}} < {{{5}}}={{{36}}}°

{{{m}}}< {{{3}}} = {{{m}}}< {{{4}}} = {{{2}}}*< {{{36}}}={{{72}}}°


and if {{{m}}} < {{{ 6}}} = < {{{2}}} + {{{12}}}° , we have
{{{m}}} < {{{ 6}}} =  {{{12+36}}}=  {{{48}}}°

{{{m}}} < {{{DEB}}}={{{180-(48+36)=96}}}°

{{{m}}}< {{{ 1}}}= {{{36+48}}}°= {{{84}}}°


so, {{{m}}}< {{{ 1}}}= {{{84}}}°


check if the sum of {{{m}}} < {{{DEB}} and {{{m}}}< {{{ 1}}} is {{{180}}}°


{{{m}}} < {{{DEB}} + {{{m}}}< {{{ 1}}}={{{96+84}}}°={{{180}}}°