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How many sldes does a regular polygon have If each exterior angle measures 72? O 8 sides O 7 sides O 4 sides O 5 sides

How many sldes does a regular polygon have If each exterior angle measures 72? O 8 sides O 7 sides O 4 sides O 5 sides

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Understanding the Geometry of Polygons: Exterior Angles** **Question:** How many sides does a regular polygon have if each exterior angle measures 72°? **Options:** - O 8 sides - O 7 sides - O 4 sides - O 5 sides **Explanation:** To determine the number of sides in a regular polygon where each exterior angle measures 72°, we need to utilize the property of the sum of exterior angles of any polygon. The sum of the exterior angles of any polygon is always 360°. The formula for finding the measure of an exterior angle of a regular polygon is: \[ \text{Exterior Angle} = \frac{360^\circ}{n} \] where \( n \) is the number of sides. Given that the exterior angle is 72°, we can set up the equation: \[ 72° = \frac{360^\circ}{n} \] Solving for \( n \) gives: \[ n = \frac{360^\circ}{72^\circ} = 5 \] Thus, the correct answer is: \[ \boxed{5 \text{ sides}} \]
Transcribed Image Text:**Understanding the Geometry of Polygons: Exterior Angles** **Question:** How many sides does a regular polygon have if each exterior angle measures 72°? **Options:** - O 8 sides - O 7 sides - O 4 sides - O 5 sides **Explanation:** To determine the number of sides in a regular polygon where each exterior angle measures 72°, we need to utilize the property of the sum of exterior angles of any polygon. The sum of the exterior angles of any polygon is always 360°. The formula for finding the measure of an exterior angle of a regular polygon is: \[ \text{Exterior Angle} = \frac{360^\circ}{n} \] where \( n \) is the number of sides. Given that the exterior angle is 72°, we can set up the equation: \[ 72° = \frac{360^\circ}{n} \] Solving for \( n \) gives: \[ n = \frac{360^\circ}{72^\circ} = 5 \] Thus, the correct answer is: \[ \boxed{5 \text{ sides}} \]
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