anonymous
  • anonymous
An exterior angle of a regular polygon cannot have what measure? a.90 b.30 c.40 d.120 e.50
Geometry
schrodinger
  • schrodinger
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mathstudent55
  • mathstudent55
The sum of the measures of the interior angles of a polygon depends on the number of sides. The sum of the measures of exterior angles of a polygon (taken one per vertex) is 360, no matter how many sides the polygon has. A regular polygon has congruent interior angles and congruent exterior angles. Therefore, the measure of an exterior angle of a regular polygon must be a factor of 360. Look at the choices you were given. Any number that is not a factor of 360 cannot be the measure.
mathmate
  • mathmate
The issue here is the definition of "regular" polygon. https://www.mathsisfun.com/definitions/regular-polygon.html Since the sum of exterior angles must add up to 360 degrees AND for a regular polygon, all interior (therefore exterior) angles must be equal, so the exterior angles of a \(regular\) polygon must equal 360 divide by an integer \(\ge\)3. So look for which angles canNOT be obtained by 360 divided by an integer.

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