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What is the sum of the measures of the exterior angles of any convex polygon?

A. [tex]$720^{\circ}$[/tex]
B. [tex]$180^{\circ}$[/tex]
C. [tex][tex]$360^{\circ}$[/tex][/tex]
D. [tex]$90^{\circ}$[/tex]

Sagot :

GinnyAnsweridn
To determine the sum of the measures of the exterior angles of any convex polygon, follow this geometric property:

The sum of the measures of the exterior angles of any convex polygon, regardless of the number of sides, is always the same. Here’s why:

1. An exterior angle of a polygon is formed by extending one side of the polygon at one vertex.
2. Each exterior angle has a corresponding interior angle, and these two angles together form a linear pair, summing up to [tex]\( 180^{\circ} \)[/tex].
3. If you go around the polygon and sum all exterior angles, you effectively make one complete rotation around the polygon, which is [tex]\( 360^{\circ} \)[/tex].

Therefore, the sum of the exterior angles of any convex polygon is always:

[tex]\[ 360^{\circ} \][/tex]

So, the correct answer is:
C. [tex]\( 360^{\circ} \)[/tex]
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