In any polygon, the exterior angle formed by extending one side is equal to the sum of the two interior angles that are adjacent to the side being extended. However, it's often more straightforward to use the property that the sum of the measures of the exterior angles of any polygon is always \(360^\circ\).
For a pentagon, the formula for finding the measure of one exterior angle is:
\[ \text{Exterior angle} = \frac{360^\circ}{n} \]
where \(n\) is the number of sides.
For a pentagon, \(n = 5\):
\[ \text{Exterior angle} = \frac{360^\circ}{5} = 72^\circ \]
However, since you are asking for the angle formed by extending one side, we cannot give a unique measure without knowing the specific interior angles of the pentagon. The exterior angle will vary depending on the shape of the pentagon.
If you're looking for a general measure of the exterior angle formed specifically at the vertex of the pentagon when one side is extended, please provide more details regarding the interior angles or any specific case of the pentagon.
In summary, the measure of the exterior angle when a side of a pentagon is extended can vary depending on the shape of the pentagon. The calculation of \(72^\circ\) is for a regular pentagon.
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