Question 1123201: Interior angle of a hexagon is 165degree and remaining each interior angle is of measure xdegree then find measure of all the remaining angel?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the sum of the interior angles of a hexagon is 4 * 180 = 720 degrees.
if one of those angles is 165 degrees, then the remaining 5 angles must be equal to 720 - 165 = 555 degrees because 555 + 165 = 720
if you divide 555 by 5, you get 111 degrees.
one of the internal angles of the hexagon is 165 degrees and the remaining 5 angles are 111 degrees each.
this is because the sum of the interior angles of a polygon is the same, whether or not the polygon is regular.
the same formula applies:
the sum of the interior angles is (n-2) * 180)
for a hexagon, that becomes 4 * 180 = 720 degrees.
for a triangle that becomes 1 * 180 = 180 degrees.
for a quadrilateral, that becomes 2 * 180 = 360 degrees.
for a pentagon, that becomes 3 * 180 = 540 degrees degrees.
the same formula applies to a polygon with any number of sides, whether or not that polygon is regular.
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