Question 1014929: A triangle has exterior angles of 108 and 145 degrees. How many degrees is the third exterior angle?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the sum of the exterior angles of a polygon is always 360 degrees.
since two of the angles = 108 and 145, the third must be the difference between those angles and 360 degrees.
108 + 145 = 253.
360 - 253 = 107 degrees.
the three external angles are 108 + 145 + 107 = 360 degrees.
the sum of the internal angles of a triangle is 180 degrees.
each external angle is supplementary to its corresponding internal angles.
the internal angles are therefore 180 - 108 + 180 - 145 + 180 - 107 = 72 + 35 + 73 = 180.
the interesting thing about the sum of the external angles is that it is always 360 degrees, regardless of the polygon.
it doesn't matter if the polygon is a triangle, or a quadrilateral, or a pentagon, of a hexagon, or whatever.
the sum of the exterior angles will always be 360 degrees.
here's a reference.
https://www.mathsisfun.com/geometry/exterior-angles-polygons.html
this reference givers an interesting prerspective as to why the sum of the exterior angles of a polygon is always 360 degrees.
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