Answered

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What is the sum of the exterior angles of a convex polygon?

A. [tex]\(360n\)[/tex]
B. [tex]\(180\)[/tex]
C. [tex]\(180(n-2)\)[/tex]
D. None of the other answers are correct
E. [tex]\(360\)[/tex]

Sagot :

GinnyAnswer
To determine the sum of the exterior angles of a convex polygon, it's important to understand some fundamental properties of polygons.

1. The exterior angle of a polygon is formed by extending one of its sides and measuring the angle between the extended line and the next side.
2. A crucial property of polygons is that the sum of their exterior angles, for any convex polygon, is always constant, regardless of the number of sides.

Here's a step-by-step explanation:

1. Consider a convex polygon with [tex]\( n \)[/tex] sides.
2. When moving around the polygon, turning at each vertex, the total amount turned in one complete cycle (one full turn around the polygon) is 360 degrees.
3. Therefore, no matter how many sides the polygon has, the sum of all the exterior angles will always be equal to one complete turn, which is 360 degrees.

Thus, the correct answer is:
360.
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