Question 1118128
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According to the condition, the interior angle is 5x, while the exterior angle is 2x,

where x is (an unknown) common measure of the two angles.



Since interior and exterior angles are supplementary, you have

2x + 5x = 180 degrees,  or  7x = 180 degrees,  i.e.  x = {{{180/7}}}.    (1)



Next, the sum of exterior angles is 360 degrees:

n*(2x) = 360 degrees,  or  n = {{{360/(2x)}}}.    (2)



Substitute here x = {{{180/7}}} from (2). You will get

n = {{{360/(2*(180/7))}}} = {{{(360*7)/(2*180)}}} = 7.


<U>Answer</U>.  The number of sides of the polygon is 7.
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