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Geometry
> *** G. 3 Exterior angles of polygons MQ7
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quad Watch a video (D)
The diagram shows a convex polygon.
What is the sum of the exterior angle measures, one at each vertex, of this polygon?
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Geometry $>\star$ G. $3$ Exterior angles of polygons MQ $7$ $\newline$ Learn with an example $\smile$ or $\quad$ Watch a video (D) $\newline$ The diagram shows a convex polygon. $\newline$ What is the sum of the exterior angle measures, one at each vertex, of this polygon? $\newline$ Submit

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Identify and classify polygons

Full solution

Q. Geometry

>\star

G.

3

Exterior angles of polygons MQ

7

\newline

Learn with an example

\smile

or

\quad

Watch a video (D)

\newline

The diagram shows a convex polygon.

\newline

What is the sum of the exterior angle measures, one at each vertex, of this polygon?

\newline

Submit

Property of Exterior Angles: The sum of the exterior angles of any convex polygon is a well-known fact in geometry. Regardless of the number of sides, the sum of the exterior angles of a convex polygon is always $360$ degrees. This is because each exterior angle forms a linear pair with an interior angle, and the sum of the angles in a linear pair is $180$ degrees. Since the interior angles sum up to $(n-2)\times180$ degrees for an $n$ -sided polygon, and there are $n$ such linear pairs, the exterior angles must sum up to $360$ degrees to maintain this relationship.
Calculation Not Required: No further calculations are needed since this is a property of convex polygons that does not depend on the number of sides the polygon has. Therefore, we can conclude that the sum of the exterior angle measures, one at each vertex, of this convex polygon is $360$ degrees.

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