Answer:
360°
Explanation:
You want the sum of the measures of the exterior angles of a regular pentagon.
Exterior angles
The sum of exterior angles of any convex polygon is 360°.
The sum of measures of exterior angles of a regular pentagon is 360°.
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Additional comment
The sum of interior angles of an n-gon is given by 180°(n -2). When the n-gon is regular, each of the interior angles is ...
(180°(n -2))/n = 180° -360°/n
The corresponding exterior angle is the supplement of this:
180° -(180° -360°/n) = 360°/n
So, the sum of n of them is ...
n(360°/n) = 360° . . . . . . sum of exterior angles
This derives the sum of exterior angles from the formula for interior angles. That formula is actually derived from the fact that exterior angles of any convex polygon total 360°. That is, we don't have to assume that the polygon is regular, but it makes this demonstration of the relationships simpler.
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