Question

An exterior angle of a regular polygon cannot have what measure?

a.90
b.30
c.40
d.120
e.50

Answer 1

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.

Answer 2

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.