Florida Teacher Certification Examinations (FTCE) Subject Area Practice Test

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Prepare for the Florida Teacher Certification Examinations. Enhance your readiness with comprehensive questions and answers, accessible hints, and detailed explanations. Ace your test and set the stage for a successful teaching career in Florida!

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A regular polygon has eight sides; what is the measure of each exterior angle?

90 degrees
45 degrees
135 degrees
180 degrees

The correct answer is: 135 degrees

To find the measure of each exterior angle of a regular polygon, you can use the formula: \[ \text{Exterior angle} = \frac{360^\circ}{n} \] where $ n $ is the number of sides of the polygon. In this case, since the polygon has eight sides ($ n = 8 $), you can substitute that value into the formula: \[ \text{Exterior angle} = \frac{360^\circ}{8} = 45^\circ \] Exterior angles of any polygon are supplementary to the interior angles, meaning every exterior angle is the angle formed between one side of the polygon and the extension of its adjacent side. In the context of an octagon, or any regular polygon, each exterior angle is crucial for understanding properties like symmetry and rotational characteristics. The measure of each exterior angle is significant in various applications, such as tiling, construction, and design where precise angles are fundamental. The correct calculated measure of each exterior angle for a regular polygon with eight sides is 45 degrees, reflecting the regular spaced distribution of angles around the vertex points of the polygon.