Question 1129631

by definition, the sum of the angles for each quadrilateral is {{{360}}}°
the sum of the {{{two}}} consecutive angles of a parallelogram have to be equal to {{{180}}} degrees

let {{{x}}} = one of the angles and let{{{ y}}} = the other angle.

{{{x + y = 180}}}

the ratio of one of these angles to the other is {{{4/5}}}

this means that {{{x/y = 4/5}}}

solve for {{{x}}} to get {{{x = (4/5) y}}}

then {{{x + y = 180}}} becomes
 
{{{(4/5) y + y = 180}}} ....solve for {{{y}}}

{{{(4/5) y +(5/5) y = 180}}}

 {{{(9/5) y = 180}}}

{{{ y = 180/(9/5)}}}

{{{ y = (180*5)/9}}}

{{{ y = (cross(180)20*5)/cross(9)}}}

{{{ y = 100}}}

then, {{{x + 100 = 180}}}=> {{{x=80}}}

the sum of two consecutive angles is equal to {{{100 + 80 = 180}}}
this confirms the solution is correct.

check the ratio:

{{{80/100=4/5}}}
{{{8/10=4/5}}}
{{{4/5=4/5}}}=> proves that angles of a parallelogram are in the ratio {{{4:5}}}