To find the measure of the exterior angle formed by extending one side of a pentagon, we can use the exterior angle theorem. The exterior angle of a polygon is equal to the sum of the two remote interior angles.
For a pentagon, the formula to find the measure of an exterior angle is:
\[ \text{Exterior angle} = 180^\circ - \text{Interior angle} \]
However, if we are simply asked about the measure of one exterior angle, we can also determine that the sum of the exterior angles for any polygon is always \(360^\circ\).
For a regular pentagon, the measure of each exterior angle would be:
\[ \text{Measure of each exterior angle} = \frac{360^\circ}{n} \] where \(n\) is the number of sides (which is 5 for a pentagon).
Calculating it, we have:
\[ \text{Measure of each exterior angle} = \frac{360^\circ}{5} = 72^\circ \]
Thus, when one side is extended, the exterior angle formed is
\[ \text{The exterior angle is } 72^\circ. \]
If you were looking for the measure of a specific angle, feel free to clarify!
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