Question 658001
Given: <{{{EAT}}} and <{{{DAT}}} are adjacent
Given: <{{{EAT}}} is {{{5x}}} larger than <{{{DAT}}}
Given: <{{{EAT = 5x}}}
Given: <{{{DAT = 4y}}}
Given: <{{{EAD = 6y+4x+4}}}
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Given: <{{{EAT = 5x}}}
Given: <{{{DAT = 4y}}}

if <{{{EAT}}} is {{{5x}}} larger than <{{{DAT}}}, and if given that <{{{EAT = 5x}}} and <{{{DAT = 4y}}}, then

{{{5x+ 5x =4y}}}

{{{10x=4y}}}.......solve for {{{x}}}..->...{{{x=(4/10)y=(2/5)y}}}

it is also given that:

{{{6y+4x+4=5x+4y}}}....plug in  {{{x=(2/5)y}}} and solve for {{{y}}}

{{{6y+4*(2/5)y+4=5*(2/5)y+4y}}}

{{{6y+1.6y+4=2y+4y}}}

{{{6y+1.6y-2y-4y=-4}}}

{{{7.6y-6y=-4}}}

{{{1.6y=-4}}}

{{{y=-4/1.6}}}

{{{highlight(y=-2.5)}}}.............negative angle (rotates  in clockwise direction)

find {{{x}}}:

{{{x=(2/5)(-2.5)}}}

{{{x=-1}}}...........also negative angle.


check:

{{{6y+4x+4=5x+4y}}}

{{{6(-2.5)+4(-1)+4=5(-1)+4(-2.5)}}}

{{{-15-4+4=-5-10}}}

{{{-15=-15}}}

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<{{{EAT}}} is {{{5x}}} larger than <{{{DAT}}}

{{{5x+ 5x =4y}}}

{{{-5-5=4(-2.5)}}}

{{{-10=-10}}}