Question 935953
The exterior angle is supplemental to the adjoining interior angle.

 if an interior angle {{{alpha}}} and exterior angle {{{gamma}}}, then


{{{alpha+gamma=180}}}.........eq.1

{{{alpha/gamma=4/5}}}.........eq.2
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{{{alpha/gamma=4/5}}}.........eq.2 ...solve for {{{alpha}}}

{{{alpha=(4/5)gamma}}}....substitute in eq.1

{{{(4/5)gamma+gamma=180}}}.........eq.1 ...solve for {{{gamma}}}

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

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

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

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

{{{highlight(gamma=100)}}}...- exterior angle

then  {{{alpha=180-100}}}=>{{{highlight(alpha=80)}}}...- interior angle


check ratio:

{{{80:100=4:5}}}

{{{80/100=4/5}}}

{{{4/5=4/5}}}